Question

The displacement (in meters) of a particle moving in a straight line is given by the equation of motion
s = 1/t^2,
where t is measured in seconds. Find the velocity of the particle at times
t = a, t = 1, t = 2, and t = 3.

Answer 1

Answer:

• -2/a³ m/s
• -2 m/s
• -1/4 m/s
• -2/27 m/s

Step-by-step explanation:

The velocity is the derivative of position:

  v = ds/dt = (d/dt)(t^-2) = -2t^-3

For t=a, the velocity is

  -2a^-3 = -2/a³ . . . . meters per second

For t=1, the velocity is ...

  -2·1³ = -2 . . . . meters per second

For t=2, the velocity is ...

  -2·2^-3 = -2/8 = -1/4 . . . . meters per second

For t=3, the velocity is ...

  -2·3^-3 = -2/27 . . . . meters per second