Question

A timer is started as a car passes a reference line, so that the distance traveled s = 0 when time t = 0. It takes 3 seconds for the car to travel 18 meters from the reference line and 8 seconds to travel 50 meters from the reference line. Calculate the car's initial velocity and acceleration.

Answer 1

Solution:

From the given information,

Let the initial velocity be u and acceleration be a

The kinematic equation for car movement,

S(t) = S₁ + ut + 1/2 at²

Given,

Condition 1 : S = 0 at t = 0 S₁ = 0

Condition 2 : S = 18 m at t = 3 s

18 = 3u + 0.5*a*3²

3u + 4.5 a = 18 -----[1]

Condition 3 : S = 50 m at t = 8 s

50 = 8u + 0.5a*8²

8u + 32a = 50 -----[2]

Solving equation [1] and [2]

u = 5.85 m/s and a = 0.1 m/s².

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