Question

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?

Answer 1

Step-by-step explanation:

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Answer 2

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

Step-by-step 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

`t = (-b \ \ +/- \ \ √(b^2 - 4ac) )/(2a) \\\\t = (-12.5 \ \ +/- \ \ √(12.5^2 - (4* 2.61 * -15)) )/(2* 2.61)\\\\t = 0.9937 \ s \ \ \ or \ \ \ -5.78 \ s\\\\time \ can \ only \ be \ positive;\\\\t \approx \ 1\ s`

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