Question

17 a particle moves along the x-axis in such a way that its position at any instant is given by

x−5t2+1

, where

x

is in metres and

t

is in seconds. calculate the instantaneous velocity at 2s.

20ms−1

30ms−1

50ms−1

25ms−1

Answer 1

Answer on Question 56261, Physics, Mechanics, Relativity

Question:

A particle moves along the $x$-axis in such a way that its position at any instant is given by $x = 5t^2 + 1$, where $x$ is in metres and $t$ is in seconds. Calculate the instantaneous velocity at $2s$.

a) $20ms^{-1}$

b) $30ms^{-1}$

c) $50ms^{-1}$

d) $25ms^{-1}$

Solution:

By the definition of the instantaneous velocity we have:

$$v = \frac{dx}{dt} = \frac{d(5t^2 + 1)}{dt} = 10t.$$

Then, the instantaneous velocity at $t = 2s$ will be:

$$v(2s) = 10 \cdot 2 = 20ms^{-1}$$

Answer:

a) $20ms^{-1}$

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