Speed, velocity, uniform and non-uniform motion — practice questions

Question 1 · difficulty L2 · understanding

The position of a particle related to time is given by $x=\left(5 t^{2}-4 t+5\right) \mathrm{m}$. The magnitude of velocity of the particle at $t=2 s$ will be :

• A. $14 \mathrm{~ms}^{-1}$
• B. $16 \mathrm{~ms}^{-1}$
• C. $10 \mathrm{~ms}^{-1}$
• D. $06 \mathrm{~ms}^{-1}$

Question 2 · difficulty L2 · understanding

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:

• A. $$5 \mathrm{~ms}^{-1}$$
• B. $$12.5 \mathrm{~ms}^{-1}$$
• C. $$62.5 \mathrm{~ms}^{-1}$$
• D. $$25 \mathrm{~ms}^{-1}$$

Question 3 · difficulty L2 · understanding

A person travels $$x$$ distance with velocity $$v_{1}$$ and then $$x$$ distance with velocity $$v_{2}$$ in the same direction. The average velocity of the person is $$\mathrm{v}$$, then the relation between $$v, v_{1}$$ and $$v_{2}$$ will be.

• A. $$\mathbf{V}=\mathbf{V}_{1}+\mathbf{V}_{2}$$
• B. $$V=\frac{v_{1}+V_{2}}{2}$$
• C. $$\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}$$
• D. $$\frac{2}{\mathrm{~V}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}$$

Question 4 · difficulty L2 · understanding

An object moves with speed $$v_1,v_2$$ and $$v_3$$ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

• A. $${{{v_1}{v_2}{v_3}} \over {3({v_1}{v_2} + {v_2}{v_3} + {v_3}{v_1})}}$$
• B. $${{({v_1} + {v_2} + {v_3})} \over 3}$$
• C. $${{({v_1} + {v_2} + {v_3})} \over {3{v_1}{v_2}{v_3}}}$$
• D. $${{3{v_1}{v_2}{v_3}} \over {({v_1}{v_2} + {v_2}{v_3} + {v_3}{v_1})}}$$

Question 5 · difficulty L2 · understanding

A vehicle travels $4 \mathrm{~km}$ with speed of $3 \mathrm{~km} / \mathrm{h}$ and another $4 \mathrm{~km}$ with speed of $5 \mathrm{~km} / \mathrm{h}$, then its average speed is

• A. $3.75 \mathrm{~km} / \mathrm{h}$
• B. $4.25 \mathrm{~km} / \mathrm{h}$
• C. $3.50 \mathrm{~km} / \mathrm{h}$
• D. $4.00 \mathrm{~km} / \mathrm{h}$

Question 6 · difficulty L2 · understanding

The distance travelled by a particle is related to time t as $$x=4\mathrm{t}^2$$. The velocity of the particle at t=5s is :-

• A. $$\mathrm{25~ms^{-1}}$$
• B. $$\mathrm{20~ms^{-1}}$$
• C. $$\mathrm{8~ms^{-1}}$$
• D. $$\mathrm{40~ms^{-1}}$$

Question 7 · difficulty L2 · understanding

A car travels a distance of '$$x$$' with speed $$v_1$$ and then same distance '$$x$$' with speed $$v_2$$ in the same direction. The average speed of the car is :

• A. $${{{v_1}{v_2}} \over {2({v_1} + {v_2})}}$$
• B. $${{2{v_1}{v_2}} \over {{v_1} + {v_2}}}$$
• C. $${{2x} \over {{v_1} + {v_2}}}$$
• D. $${{{v_1} + {v_2}} \over 2}$$

Question 8 · difficulty L2 · understanding

If $$\mathrm{t}=\sqrt{x}+4$$, then $$\left(\frac{\mathrm{d} x}{\mathrm{~d} t}\right)_{\mathrm{t}=4}$$ is :

• A. 4
• B. zero
• C. 8
• D. 16

Question 9 · difficulty L2 · understanding

The instantaneous velocity of a particle moving in a straight line is given as $$V = \alpha t + \beta {t^2}$$, where $$\alpha$$ and $$\beta$$ are constants. The distance travelled by the particle between 1s and 2s is :

• A. 3$$\alpha$$ + 7$$\beta$$
• B. $${3 \over 2}\alpha + {7 \over 3}\beta$$
• C. $${\alpha \over 2} + {\beta \over 3}$$
• D. $${3 \over 2}\alpha + {7 \over 2}\beta$$

Question 10 · difficulty L2 · understanding

A person travelling on a straight line moves with a uniform velocity $v_1$ for a distance $x$ and with a uniform velocity $v_2$ for the next $\frac{3}{2} x$ distance. The average velocity in this motion is $\frac{50}{7} \mathrm{~m} / \mathrm{s}$. If $v_1$ is $5 \mathrm{~m} / \mathrm{s}$ then $v_2=$ __________ $\mathrm{m} / \mathrm{s}$.