Question 23: Motion in 1D

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 $$\mathrm{t}=5 \mathrm{~s}$$ will be:

Accepted Answer

The distance traveled by an object in time $$t$$ is given by the equation $$s = (2.5)t^2$$. To find the instantaneous speed at a specific time, we need to find the first derivative of the distance function with respect to time, which gives us the velocity function:
$$v(t) = \frac{ds}{dt}$$
Differentiating the given equation with respect to $$t$$:
$$v(t) = \frac{d}{dt} (2.5)t^2 = 2(2.5)t = 5t$$
Now, we can find the instantaneous speed at $$t = 5 \mathrm{~s}$$ by plugging the value into the velocity function:
$$v(5) = 5(5) = 25 \mathrm{~m/s}$$
The instantaneous speed of the object at $$t = 5 \mathrm{~s}$$ is $$25 \mathrm{~m/s}$$.

Answer

$$5 \mathrm{~ms}^{-1}$$

Answer

$$12.5 \mathrm{~ms}^{-1}$$

Answer

$$62.5 \mathrm{~ms}^{-1}$$

Answer

$$25 \mathrm{~ms}^{-1}$$

Motion in 1D

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

Choose the correct answer: