Question

A car, initially traveling 10m/s, gains speed at a rate of 2m/s2 while traveling 56m. Find how long the car was traveling and the car’s final velocity.

Please show work very confused

Answer 1

Time travel = 4 s

The car’s final velocity : 18 m/s

Further explanation

Given

initial velocity=vo= 10 m/s

acceleration = a = 2 m/s²

distance=d = 56 m

Required

Time travel and the final velocity

Solution

• time travel

$\tt d=vo.t+\dfrac{1}{2}at^2\\\\56=10.t+\dfrac{1}{2}.2.t^2\\\\56=10t+t^2\\\\t^2+10t-56=0\\\\(t-4)(t+14)=0\\\\t=4,t=-14\rightarrow take~a~positive~value~t=4~s$

• the car’s final velocity.

$\tt v_f=v_i+at\\\\v_f=10+2.4\\\\V_f=18~m/s$