A car is moving along a straight road. Its displacement as a function of time is as shown. Find its velocity at t = 3 s and at t = 7 s.

a ) 12 m /s, -8 m /s .
b ) 12 m /s, 8 m /s .
c ) 6 m /s, 4 m /s .
d ) 6 m /s, -4 m /s .

The equation s = 2 t² describes the motion at the instant t = 3 s. The velocity is given by,

The s - t graph, is a straight line between t = 6 s to t = 10 s . This line can be represented by the equation

    s = m t + c.

where m and c are the slope and the intercept on the displacement axis. This line passes through the points ( 6 s, 32 m) and (10 s,0 m). Substituting these in the above equation and solving the resulting simultaneous linear equations in 2 variables for the two constants m and c,we get,

   s = - 8 t + 80 .

And hence the velocity at t = 7 s is given by,