A car of mass 1200 kg is being towed horizontally on the end of a horizontal cable the car accelerates uniformly from rest to a speed of 15ms-1 in a distance of 75m show that the accleration of t?

Answer 1

A car of mass 1200 kg is being towed horizontally on the end of a horizontal cable the car accelerates uniformly from rest to a speed of 15ms-1 in a distance of 75m show that the accleration of t?

Motion formulas

vfinal = vinitial + acceleration * time

vf = vi + a * t

vf - vi = a * t

t = (vf - vi ) ÷ a

average velocity = (vi + vf) ÷ 2

distance = average velocity * time

d = (vi + vf) ÷ 2t

t = 2d ÷ (vi + vf)

Set the 2 equations equal to t, equal to each other.

(vf - vi ) ÷ a = 2d ÷ (vi + vf)

This would look better as a proportion, but wiki doesn't copy symbols!

Cross multiply and divide

(vf - vi ) * (vi + vf) = 2*a*d

vf2 - vi2 = 2*a*d

vf2 = vi2 +2*a*d

Your question:

Mass = 1200Kg

Distance = 75m

vi = 0 m/s

change in velocity = (vf - vi) = 15m/s - 0 /s = 15m/s

(vf - vi) = 15m/s

vf2 = vi2 + 2*a*d

vi2 = 0

vf2 = 2*a*d

152 = 2*a*75 a = 1.5 m/s

vf = vi + at

t = (vf - vi)÷ a

t = 15m/s ÷ 1.5 m/s2 = 10 seconds

Force = mass * acceleration F = 1200kg * 1.5 m/s2 =

F = 1800 Newtons