In order to merge into highway traffic, a car accelerates along a 100.0 m on ramp from rest to 25.0 m/s. How much time does this take?

8 seconds

Explanation:

Using the equation of motion v² = u²+2as to get the acceleration of the body.

v = final velocity (in m/s)

u = initial velocity (in m/s)

a = acceleration (in m/s²)

s = distance covered by the car (in metres)

Given u = 0m/s (the car accelerates from rest)

v = 25m/s

S = 100.0m

on substituting,

25² = 0²+2 (100) a

625 = 200a

a = 625/200

a = 3.125 m/s²

Since Acceleration = change in velocity/time

3.125 = 25-0/time

3.125t = 25

t = 25/3.125

t = 8 seconds

It takes 8 seconds to merge into highway traffic.