Question

Two cars start from rest. Both cars accelerate at a constant rate for a certain period. Car 1’s acceleration is twice Car 2’s acceleration; Car 2 accelerates for twice as long as Car 1. Which car covers more distance during its period of acceleration? By what factor?

assume g=10m/s^2

Answer 1

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Answer 2

SOLUTION :

Let acceleration, time and distance covered  of car1 be a1,  t1, d1  respectively.

Let acceleration, time  and distance covered of car2 be a2,  t2 and d2 respectively.

Initial speed for both cars = 0 m/s

So, 

a2 = a1 /2 

t2 = 2 t1 

d1 = 1/2 a1 t1^2

d2 = 1/2 a2 t2^2 = 1/2 (a1 / 2) * (2 t1)^2 = 4  a1 t1^2 

d2 / d1 = 8 

So, distance covered by car 2 is more. It is 8 times the distance covered by car 1 . (ANSWER

Answer 3

SOLUTION :

Let acceleration, time and distance covered  of car1 be a1,  t1, d1  respectively.

Let acceleration, time  and distance covered of car2 be a2,  t2 and d2 respectively.

Initial speed for both cars = 0 m/s

So, 

a2 = a1 /2 

t2 = 2 t1 

d1 = 1/2 a1 t1^2

d2 = 1/2 a2 t2^2 = 1/2 (a1 / 2) * (2 t1)^2 =  a1 t1^2 

d2 / d1 = 2 

So, distance covered by car 2 is more. It is 2 times the distance covered by car 1 . (ANSWER)