The radius of Mercury is 2400 km, and the acceleration due to gravity at its surface is 3.7 m/s$^{2}$. What is the mass of Mercury?

Can you cite an example wherein the acceleration of a body is opposite in direction to its velocity? If so, what is your example?

Use the given position function to find velocity and acceleration. $s(t)=-9.8 t^{2}-22 t+6$

The weight of an object is directly proportional to (a) its mass , (b) its inertia , (c) the acceleration due to gravity, (d) all of the preceding.

The Phoenix with a mass of $350$ kg was a spacecraft used for exploration of Mars. Determine the weight of the Phoenix, in N,

$$\begin{array}{l l } \text{(a) on the surface of Mars where the acceleration of gravity is $3.73 \hspace{1mm} m/s^2$}\\ \text{(b) on Earth where the acceleration of gravity is $9.81 \hspace{1mm} m/s^{2}$. }\\ \end{array}$$

Calculate the acceleration of a ball that starts from rest and rolls down a ramp and gains a speed of $25 {m} / {s}$ in $5{s}$.

A motorcycle ride consists of two segments. During segment 1 , the motorcycle starts from rest, has an acceleration of $+2.6 \mathrm{~m} / \mathrm{s}^2$, and has a displacement of $+120 \mathrm{~m}$. Immediately after segment 1 , the motorcycle enters segment 2 and begins slowing down with an acceleration of $-1.5 \mathrm{~m} / \mathrm{s}^2$ until its velocity is $+12 \mathrm{~m} / \mathrm{s}$. A drag racer, starting from rest, speeds up for $402 \mathrm{~m}$ with an acceleration of $+17.0 \mathrm{~m} / \mathrm{s}^2$. A parachute then opens, slowing the car down with an acceleration of $-6.10 \mathrm{~m} / \mathrm{s}^2$. How fast is the racer moving $3.50 \times 10^2 \mathrm{~m}$ after the parachute opens?

If an object has an acceleration of $10\, \mathrm{\frac{m}{s^{2}}}$ and a mass of $30\, \mathrm{kg}$, what is its force?

At Earth’s surface, the acceleration due to gravity is approximately $g=9.8\ \mathrm{m}/\mathrm{s}^2$(with local variations). However, acceleration decreases with distance from the surface according to Newton’s law of gravitation. At a distance of y meters from Earth’s surface, the acceleration is given by $a(y)=- \frac { g } { ( 1 + y / R ) ^ { 2 } }$, where $R=6.4 \times 10 ^ { 6 }$ m is the radius of Earth.

Use the Chain Rule to show that $\frac { d v } { d t } = \frac { 1 } { 2 } \frac { d } { d y } \left( v ^ { 2 } \right)$.

A car experiences a centripetal acceleration of 4.3 m/s^2 as it rounds a corner with a speed of 11 m/s. What is the radius of the corner?

In these exercises r(t) is the position vector of a particle moving in the plane. Find the velocity, acceleration, and speed at an arbitrary time t . Then sketch the path of the particle together with the velocity and acceleration vectors at the indicated time t.

$$\mathbf { r } ( t ) = e ^ { t } \mathbf { i } + e ^ { - t } \mathbf { j }$$

; t=0

Newton’s law of gravitation states that any two objects exert a gravitational force on each other due to their masses,

$$F _ { g } = G \frac { m _ { 1 } m _ { 2 } } { r ^ { 2 } }$$

, where F is the gravitational force, G is a constant (the universal gravitational constant),

$$m_1$$

and

$$m_2$$

are the masses of the objects, and r is the separation distance between the centres of objects. The mass of Mercury is 2.2 times greater than the mass of Pluto. Pluto is 102.1 times as far from the Sun as Mercury. How many times greater is the gravitational force between the Sun and Mercury than the gravitational force between the Sun and Pluto?

A student asks a friend the following question:
"How is acceleration different from velocity?"
Which of the following answers would best help the student understand acceleration? Why do you think so? Ask the question yourself to some friends and think about their answers.
a. Acceleration has units of $\mathrm{m} / \mathrm{s}^2$ while velocity has units of $\mathrm{m} / \mathrm{s}$.
b. How do you describe a change in speed from 10 to $20 \mathrm{mph}$ that occurs over $2 \mathrm{~s}$ ?

Explain why an object moving along a line is slowing down when its velocity and acceleration have opposite signs.