Question

A car start from rest and move with an accelaration of 5m/s(square) for 5 second It then travel at constant velacity for 50 seconds, finally coming to rest with uniform retardation in 10 seconds Draw a velacity time graph and determine the distance covered

Answer 1

Answer on Question #38573, Physics, Mechanics

Let us examine motion on each of three parts of the distance.

I. Motion with acceleration $5\frac{m}{s^2}$ for 5 seconds. Here, velocity is $\nu = \nu_0 + at = 5t$ . For $t = 5s$ , $\nu = 5\cdot 5 = 25\frac{m}{s}$ .

II. Motion with constant velocity $\nu = 25\frac{m}{s}$ for 50 seconds.

III. Motion with retardation for 10 seconds. Using formula $\nu = \nu_{0} + at$ find the retardation, $0 = 25 + 10\cdot a\Rightarrow a = -2.5\frac{m}{s^{2}}$ . Hence, velocity as a function of time is $\nu = 25 - 2.5t$ (If time starts from zero at third part of the track).

Velocity graph is

The distance covered is sum of distances covered on each part of the road:

$S = \int_{0}^{5} 5t \, dt + 50 \cdot 50 + \int_{0}^{10} (25 - 2.5t) \, dt = 5 \frac{t^2}{2} | + 2500 + (25t - 2.5 \frac{t^2}{2})|_0^0 = 2690 \, m$ (area under the velocity curve).