Question

The distance travelled by an object in time \( t \) is given by \( s = (2.5)t^2 \). The instantaneous speed of the object at \( t = 5 \, \text{s} \) will be:

• A. 5 m/s
• B. 10 m/s
• C. 25 m/s
• D. 50 m/s

Answer 1

The Correct Option is C

We can find the velocity (v) of the particle at any time by taking the derivative of its position (x) with respect to time (t):v = dx/dt
For the given position function, x = 2.5t^2, we have:
v = d(2.5t^2)/dt = 5t
Therefore, the velocity of the particle at time t is 5t m/s.
To find the velocity at t = 5 seconds, we substitute t = 5 into the expression for v:
v = 5t = 5(5) = 25 m/s
Hence, the speed of the particle at t = 5 seconds is 25 m/s. Note that speed is the magnitude of velocity and is always non-negative, so we don't need to include a sign.
Answer. C

Answer 2

The distance travelled by the object is given as: \[ s = 2.5t^2 \] The instantaneous speed \( v \) is the derivative of distance \( s \) with respect to time \( t \): \[ v = \frac{ds}{dt} = \frac{d}{dt}(2.5t^2) = 5t \] At \( t = 5 \, \text{s} \): \[ v = 5 \times 5 = 25 \, \text{m/s}. \] Thus, the instantaneous speed of the object at \( t = 5 \, \text{s} \) is \( \boxed{25 \, \text{m/s}} \).