A motorcycle is following a car that is traveling at constant speed on a straigh

Question

A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 20.0 m/s , and the distance between them is 50.0 m. After t1 = 2.00 s , the motorcycle starts to accelerate at a rate of 4.00 m/s2 . The motorcycle catches up with the car at some time t2.

Part A

Which of the graphs (Figure 1) correctly displays the positions of the motorcycle and car as functions of time?

Part B

How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t2?t1.

Express the time numerically in seconds using three significant figures.

Part C

How far does the motorcycle travel from the moment it starts to accelerate (at time t1) until it catches up with the car (at time t2)? Should you need to use an answer from a previous part, make sure you use the unrounded value.

Answer numerically in meters using three significant figures.

Explanation / Answer

part A)for uniform motion the graph gives a straight line

for acclerated motion it gives a parabola finally they should meet at a point

obviously option a)

part b) consider relative motion S=urelt+1/2 arelt2 here urel=20-20=0 arel =4-0=4 S=50m

50 =0+1/2(t)2 ;   time t=10s

part c) smotor =ut+1/2 (t)2 =20(10)+1/2(4)(10)2

=200+200=400m

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