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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
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