Question

A car has an initial speed of 10 m/s. It then undergoes a constant acceleration of 0.05 m/s^2 over a distance of 5 km. Determine: a) The car final speed. b) The time needed to travel the 5 km.

Answer 1

(a) 24.49 m/s

(b) 289.8 s

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

Given:

u = 10 m/s

a = 0.05 m/s²

s = 5 km = 5000 m ( 1 km = 1000 m)

Considering - Equation of motion

`v^2-u^2=2as`

Applying values as:

`v^2-u^2=2as\\\Rightarrow v=√(2as+u^2)\\\Rightarrow v=√(2* 0.05* 5000+10^2)\\\Rightarrow v=24.49\ m/s`

Considering - Equation of motion

`v=u+at`

Applying values as:

`v=u+at\\\Rightarrow 24.49=10+0.05t\\\Rightarrow t=(24.49-10)/(0.05)=289.8\ s`