Q: A particle's position is given by $$x = 3.5t^3$ - 1.2t (in $$meters). What is the velocity and acceleration of the particle at $$t = 2.0\ \text{s}$$?

Velocity: $$41\ \text{m/s}$$, Acceleration: $$42\ \text{m/s}^2$$

Q: Three displacement vectors are given: $$\vec{A} is$$ $$75\ \text{cm} at$$ $$30^\circ$$ above the $$+x-$$axis, $$\vec{B} is$$ $$25\ \text{cm}$$ along the $$-x-$$axis, and $$\vec{C} is$$ $$40\ \text{cm} at$$ $$45^\circ$$ below the $$-x-$$axis. What is the magnitude and direction of the resultant vector?

$$15\ \text{cm} at$$ $$38^\circ$$ above the $$+x-$$axis

Q: The velocity of a particle is given by $$\vec{V} = (2.6t^2$ - 4)\hat{i} + (-4.5t + 8)\hat{j} (in m/s). $$What is the magnitude and direction of the acceleration at $$t = 2.0\ \text{s}$$?

$$11.3\ \text{m/s}^2$$, $$-23.4^\circ$$

Question 1

A car is moving at a constant speed of 72 km/h along a straight road. If the driver looks away for 4.0 s, how far does the car travel during this period? (Use $$1\ 	ext{km} = 1000\ 	ext{m})$$

Accepted Answer

$$80\ 	ext{m}$$

Question 2

An airplane increases its speed at an average rate of $$15\ 	ext{m/s}^2. $$How much time does it take to increase its speed from $$100\ 	ext{m/s} to$$ $$160\ 	ext{m/s}$$?

Accepted Answer

$$4.0\ 	ext{s}$$

Question 3

A particle's position is given by $$x = 3.5t^3$ - 1.2t (in $$meters). What is the velocity and acceleration of the particle at $$t = 2.0\ 	ext{s}$$?

Accepted Answer

Velocity: $$41\ 	ext{m/s}$$, Acceleration: $$42\ 	ext{m/s}^2$$

Question 4

A car starts from rest and accelerates at $$2.0\ 	ext{m/s}^2$$ for $$10\ 	ext{s}$$, then travels at the speed it reached for another $$10\ 	ext{s}$$, and finally slows to a stop with a constant acceleration of $$-2.0\ 	ext{m/s}^2. $$What is the total distance traveled?

Accepted Answer

$$400\ 	ext{m}$$

Question 5

A car increases its velocity uniformly from $$40\ 	ext{m/s} to$$ $$80\ 	ext{m/s}$$ while traveling $$200\ 	ext{m}. $$What is its acceleration?

Accepted Answer

$$12\ 	ext{m/s}^2$$

Question 6

A car is moving at $$32.0\ 	ext{m/s}. $$The driver sees an accident ahead and applies the brakes, causing the car to decelerate at $$3.50\ 	ext{m/s}^2. $$How far does the car travel before coming to a stop?

Accepted Answer

$$146\ 	ext{m}$$

Question 7

A bullet is shot straight up and returns to its starting point in $$10\ 	ext{s}. $$What is the initial speed of the bullet? (Assume $$g = 9.8\ 	ext{m/s}^2$$ and negligible air resistance.)

Accepted Answer

$$49\ 	ext{m/s}$$

Question 8

A ball is thrown downward from the top of a building with an initial speed of $$25\ 	ext{m/s}. It $$strikes the ground after $$2.0\ 	ext{s}. $$How high is the building? (Assume $$g = 9.8\ 	ext{m/s}^2$$ and negligible air resistance.)

Accepted Answer

$$70\ 	ext{m}$$

Question 9

Three displacement vectors are given: $$\vec{A} is$$ $$75\ 	ext{cm} at$$ $$30^\circ$$ above the $$+x-$$axis, $$\vec{B} is$$ $$25\ 	ext{cm}$$ along the $$-x-$$axis, and $$\vec{C} is$$ $$40\ 	ext{cm} at$$ $$45^\circ$$ below the $$-x-$$axis. What is the magnitude and direction of the resultant vector?

Accepted Answer

$$15\ 	ext{cm} at$$ $$38^\circ$$ above the $$+x-$$axis

Question 10

The velocity of a particle is given by $$\vec{V} = (2.6t^2$ - 4)\hat{i} + (-4.5t + 8)\hat{j} (in m/s). $$What is the magnitude and direction of the acceleration at $$t = 2.0\ 	ext{s}$$?

Accepted Answer

$$11.3\ 	ext{m/s}^2$$, $$-23.4^\circ$$

Question 11

A girl throws a rock horizontally with a velocity of $$10\ 	ext{m/s}$$ from a bridge. It falls $$20\ 	ext{m} to $$the water below. How far does the rock travel horizontally before striking the water? (Assume negligible air resistance.)

Accepted Answer

$$20\ 	ext{m}$$

Question 12

A child throws a ball with an initial speed of $$8.0\ 	ext{m/s} at an $$angle of $$40^\circ$$ above the horizontal. The ball leaves her hand $$1.0\ 	ext{m}$$ above the ground and the fence is $$2.0\ 	ext{m}$$ high. The ball just clears the fence while still traveling upwards. How far is the child from the fence?

Accepted Answer

$$1.6\ 	ext{m}$$

Question 13

A child throws a ball with an initial speed of $$8.0\ 	ext{m/s} at an $$angle of $$40^\circ$$ above the horizontal from $$1.0\ 	ext{m}$$ above the ground. How far from where the child is standing does the ball hit the ground?

Accepted Answer

$$7.5\ 	ext{m}$$

Question 14

For the same scenario as above, how long is the ball in flight before it hits the ground?

Accepted Answer

$$1.2\ 	ext{s}$$

Question 15

For the same scenario as above, what is the magnitude of the ball's velocity just before it hits the ground?

Accepted Answer

$$9.1\ 	ext{m/s}$$

Question 16

A car accelerates from rest at $$2.0\ 	ext{m/s}^2$$ for $$10\ 	ext{s}$$, then travels at constant speed for $$10\ 	ext{s}$$, and finally decelerates to rest at $$-2.0\ 	ext{m/s}^2. $$What is the speed of the car at the end of the first $$10\ 	ext{s}$$?

Accepted Answer

$$20\ 	ext{m/s}$$

Question 17

A bullet is shot straight up and returns to its starting point in $$10\ 	ext{s}. $$What is the maximum height reached by the bullet? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$122.5\ 	ext{m}$$

Question 18

A ball is thrown downward from a building with an initial speed of $$25\ 	ext{m/s}$$ and strikes the ground after $$2.0\ 	ext{s}. $$What is the final velocity of the ball just before impact? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$44.6\ 	ext{m/s}$$

Physics with Calculus: Step-by-Step Guidance for Kinematics and Vector Problems

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