Question

Given that the total distance travelled is 1. 4km, and the acceleration is 4m/s^2 for the first T seconds , find: a) the value of V b) the value of T

Answer 1

Explanation:

The distance, s, travelled by an object accelerating by a, for a time t, and with initial velocity u, is given by:

s = ut + (1/2)at^2

We'll assume the initial velocity for this problem is 0 (none). It accelerates from rest and continues accelerating at 4m/s^2.

We want to find the time, t, required to reach 1.4km.

s = ut + (1/2)at^2

1.4km = (0)t + (1/2)(4m/s^2)t^2

2.8km = (4m/s^2)*t^2

t^2 = (2.8km)/(4m/s^2)

t^2 = (2.8km)*(1000m/km)/(4m/s^2) [Convert km to meters]

t^2 = (2800m)/(4m/s^2)

t^2 = (700s^2)

t = 26.4 seconds 26 seconds with 2 sig figs

The velocity is given by: V = at

Velocity at 26.4 seconds is: V= (4m/s^2)*(26.4s)

V = 105.8 m/s

Average velocity is (105.8m/s - 0m/s)/2 = 59.2 m/s