The graph in the figure shows the velocity of a motorcycle police officer plotted as a function of time
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- The graph in the figure shows the velocity of a motorcycle police officer plotted as a function of time. (a) Find the instantaneous acceleration at t = 3 s, at t = 7 s, and at t = 11 s. (b) How far does that officer go in the first 5 s? The first 9 s? The first 13 s?
- A car sits in an entrance ramp to a freeway, waiting for a break in the traffic. The driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of 20 m/s when it reaches the end of the 120 m-long ramp. (a) What is the acceleration of the car? (b) How much time does it take the car to travel the length of the ramp? (c) The traffic on the freeway is moving at a constant speed of 20 m/s. What distance does the traffic travel while the car is moving the length of the ramp?
- At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.20 m/s2. At the same instance a truck, traveling with a constant speed of 20.0 m/s, overtakes and passes the car. (a) How far beyond its starting point does the car overtake the truck? (b) How fast is the car traveling when it overtakes the truck? (c) Sketch an x-t graph of the motion of both vehicles. Take x = 0 at the intersection. (d) Sketch a v-t graph of the motion of both vehicles.
- Large cockroaches can run as fast as 1.50 m/s in short bursts. Suppose you turn on the light in a cheap motel and see one scurrying directly away from you at a constant 1.50 m/s. It you start 0.90 m behind the cockroach with an initial speed of 0.80 m/s toward it, what minimum constant acceleration would you need to catch up with it when it has traveled 1.20 m, just short of safety under a counter?
- Two cars start 200 m apart and drive toward each other at a steady 10 m/s. On the front of one of them, and energetic grasshopper jumps back and forth between the cars (he has strong legs!) with a constant horizontal velocity of 15 m/s relative to the ground. The insect jumps the instant it lands, so he spends no time resting on either car. What total distance does the grasshopper travel before the cars hit?
- You are arguing over a cell phone while trailing an unmarked police car by 25m; both your car and the police car are travelling at 110km/h. Your argument diverts your attention from the police car for 2.0 s. At the beginning of that 2.0 s, the police officer begins braking suddenly at 5.0 m/s2.
(a) What is the separation between the two cars when your attention finally returns?
(b) Suppose that you take another 0.40 s to realize your danger and begin braking. If you too brake at 5.0 m/s2, what is your speed when you hit the police car?
- When a high speed passenger train traveling at 161 kilometers per hour (km/h) rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance D = 676 m ahead. The locomotive is moving at 29.0 km/h. The engineer of the high speed train immediately applies the brakes.
(a) What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided?
(b) Assume that the engineer is at x=0 when, at t=0, he first spots the locomotive. Sketch x(t) curves for the locomotive and high-speed train for the cases in which a collision is just avoided and is not quite avoided.
- The graph in the figure shows the velocity of a motorcycle police officer plotted as a function of time. (a) Find the instantaneous acceleration at t = 3 s, at t = 7 s, and at t = 11 s. (b) How far does that officer go in the first 5 s? The first 9 s? The first 13 s?
- A car sits in an entrance ramp to a freeway, waiting for a break in the traffic. The driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of 20 m/s when it reaches the end of the 120 m-long ramp. (a) What is the acceleration of the car? (b) How much time does it take the car to travel the length of the ramp? (c) The traffic on the freeway is moving at a constant speed of 20 m/s. What distance does the traffic travel while the car is moving the length of the ramp?
- At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.20 m/s2. At the same instance a truck, traveling with a constant speed of 20.0 m/s, overtakes and passes the car. (a) How far beyond its starting point does the car overtake the truck? (b) How fast is the car traveling when it overtakes the truck? (c) Sketch an x-t graph of the motion of both vehicles. Take x = 0 at the intersection. (d) Sketch a v-t graph of the motion of both vehicles.
- Large cockroaches can run as fast as 1.50 m/s in short bursts. Suppose you turn on the light in a cheap motel and see one scurrying directly away from you at a constant 1.50 m/s. It you start 0.90 m behind the cockroach with an initial speed of 0.80 m/s toward it, what minimum constant acceleration would you need to catch up with it when it has traveled 1.20 m, just short of safety under a counter?
- Two cars start 200 m apart and drive toward each other at a steady 10 m/s. On the front of one of them, and energetic grasshopper jumps back and forth between the cars (he has strong legs!) with a constant horizontal velocity of 15 m/s relative to the ground. The insect jumps the instant it lands, so he spends no time resting on either car. What total distance does the grasshopper travel before the cars hit?
- You are arguing over a cell phone while trailing an unmarked police car by 25m; both your car and the police car are travelling at 110km/h. Your argument diverts your attention from the police car for 2.0 s. At the beginning of that 2.0 s, the police officer begins braking suddenly at 5.0 m/s2.
(a) What is the separation between the two cars when your attention finally returns?
(b) Suppose that you take another 0.40 s to realize your danger and begin braking. If you too brake at 5.0 m/s2, what is your speed when you hit the police car? - When a high speed passenger train traveling at 161 kilometers per hour (km/h) rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance D = 676 m ahead. The locomotive is moving at 29.0 km/h. The engineer of the high speed train immediately applies the brakes.
(a) What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided?
(b) Assume that the engineer is at x=0 when, at t=0, he first spots the locomotive. Sketch x(t) curves for the locomotive and high-speed train for the cases in which a collision is just avoided and is not quite avoided.