Question 1

A boat is traveling north at 30 miles per hour and experiences a constant acceleration of 5 miles per hour per minute to the south for 8 minutes. What is the boat’s new velocity?

Accepted Answer

10 miles per hour south

Question 2

Given vectors $$\vec{A} = 3 \hat{i} + 4 \hat{j}$$ and $$\vec{B} = -2 \hat{i} + 3 \hat{j}$$, what is the angle $$	heta$$ between $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$57.6^\circ$$

Question 3

A soccer ball rolls along the ground and hits a wall, bouncing back. When the ball hits the wall and changes direction, which of the following is true?

Accepted Answer

velocity is not zero and acceleration is not 0

Question 4

A 10 kg box is being pulled along a frictionless floor by a rope at an angle of $$30^\circ$$ above the horizontal. The tension in the rope is 60 N. What is the acceleration of the box?

Accepted Answer

$$5.2\ \mathrm{m/s^2$}$$

Question 5

A 10 kg box is being pulled along a frictionless floor by a rope at an angle of $$30^\circ$$ above the horizontal. The tension in the rope is 60 N. What is the magnitude of the normal force exerted on the box by the ground?

Accepted Answer

Question 6

Refer to the velocity vs. time graph provided. Rank the instantaneous acceleration at moments A, B, C, D, and E from most negative to most positive.

Accepted Answer

E \u003c D \u003c A \u003c B \u003c C

Question 7

Using the velocity vs. time graph, what is the object’s displacement from $$t = 4\ \mathrm{s} to$$ $$t = 6.5\ \mathrm{s}$$?

Accepted Answer

$$-2.5\ \mathrm{m}$$

Question 8

A ball is rolling down a circular half pipe of radius $$3\ \mathrm{m}. At $$the moment shown, the ball’s speed is increasing at a rate of $$3.5\ \mathrm{m/s^2$}$$ and the total acceleration is $$6.0\ \mathrm{m/s^2$}. $$What is the ball’s speed at this moment?

Accepted Answer

$$4.2\ \mathrm{m/s}$$

Question 9

Refer to the diagram with arrows A, B, C, and D. Which arrow best represents the direction of the total acceleration at this moment?

Accepted Answer

Arrow C

Question 10

Two boxes (5 kg and 15 kg) are sitting next to each other on a flat frictionless floor. You push horizontally on the 5 kg box with 40 N of force. What is the acceleration of the system?

Accepted Answer

$$2\ \mathrm{m/s^2$}$$

Question 11

A ball is kicked at $$20\ \mathrm{m/s} at an $$angle $$30^\circ$$ above the horizontal. On its way down, it just barely passes over the top of a $$3\ \mathrm{m}$$ tall fence. How far away from you is the fence?

Accepted Answer

$$36.5\ \mathrm{m}$$

Question 12

A ball is kicked at $$20\ \mathrm{m/s} at an $$angle $$30^\circ$$ above the horizontal. What is the angle of the velocity as the ball passes over the fence?

Accepted Answer

$$-37^\circ$$

Question 13

Trey is standing still when Billy Joe runs by at $$4\ \mathrm{m/s}$$ and grabs Trey’s drumsticks. After 5 seconds, Trey accelerates at $$2\ \mathrm{m/s^2$}$$ from rest to a top speed of $$6\ \mathrm{m/s}$$ and continues at top speed. After running at top speed for $$60\ \mathrm{m}$$, Trey begins slowing down at a rate of $$0.2\ \mathrm{m/s^2$}. $$How far does Trey run before catching up to Billy Joe, assuming Billy Joe maintains a constant speed?

Accepted Answer

$$210\ \mathrm{m}$$

Question 14

Which of the following best describes the relationship between the net force and acceleration for an object of mass $$m$$?

Accepted Answer

$$\sum F = m a$$

Question 15

A car accelerates uniformly from rest to $$20\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is the magnitude of its acceleration?

Accepted Answer

$$4\ \mathrm{m/s^2$}$$

Question 16

A cyclist travels 100 m north, then 100 m east. What is the magnitude of the displacement?

Accepted Answer

$$141\ \mathrm{m}$$

Question 17

A ball is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$What is the maximum height reached by the ball? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$11.5\ \mathrm{m}$$

Physics with Calculus Exam 1 Study Guidance

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