Variable forces and motion in one dimension Quiz

1. A force depends on displacement $x$. Which form of acceleration is best?

• A. $\frac{dv}{dt}$
• B. $\frac{d^2x}{dt^2}$
• C. $v\frac{dv}{dx}$
• D. constant $a$

2. A particle of mass 2 kg starts from rest under a force $4t^2$ N. What is its speed when $t=3$?

• A. 9 m s⁻¹
• B. 18 m s⁻¹
• C. 36 m s⁻¹
• D. 6 m s⁻¹

3. A particle satisfies $\frac{dv}{dt}=-3v$ with $v=5$ when $t=0$. Which is correct?

• A. $v=5-3t$
• B. $v=5e^{3t}$
• C. $v=-15t$
• D. $v=5e^{-3t}$

4. A particle has $v\frac{dv}{dx}=6-2x$ and is at rest at $x=0$. What is its speed at $x=2$?

• A. 4 m s⁻¹
• B. 8 m s⁻¹
• C. 16 m s⁻¹
• D. 2 m s⁻¹

5. A particle is at distance $3R$ from the Earth's centre. How does the gravitational force on it compare with its weight at the surface?

• A. $\frac13$ as large
• B. $\frac16$ as large
• C. $\frac19$ as large
• D. 3 times as large