Starting from rest, a car takes 2.4 s to travel the first 15 m. Assuming a constant acceleration, how long will it take the car to travel the next 15 m?

The time it will take the car to travel the next 15 m is 1 s.

Explanation:

Given;

initial velocity of the car, u = 0

time of motion, t = 2.4 s

initial distance traveled, d = 15 m

determine the constant acceleration of the car;

d = ut  +  ¹/₂at²

15 = 0  +  (0.5 x 2.4²)a

15 = 2.88a

a = 15 / 2.88

a = 5.21 m/s²

The velocity of the car at the end of the first 15 m

v - u + at

v = 0 + 5.21 x 2.4

v = 12.5 m/s

The time to cover the next 15 m;

d₂ = vt  + ¹/₂at²

15 = 12.5t  +  (0.5 x 5.21)t²

15 = 12.5t  +  2.61t²

0 = 2.61t²  +   12.5t   -  15

Use the formula method to solve the above quadratic equation.

a = 2.61

b = 12.5

c = -15

Therefore, the time it will take the car to travel the next 15 m is 1 s.

1 a

2 b

3 b

4 d

5 d

6 d

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