Graphical Analysis of Motion

Solutions with with detailed explanations to Free SAT II Physics Practice Questions on Graphical Analysis of Motion.

Question 1 to 4 refer to the displacement vs time below.

The graph of the position x versus time t of a moving object is shown in figure 1 above . On which time interval(s) is the velocity of the moving object equal to zero?

A) (0 , 1)

B) (1 , 4)

C) (4 , 6)

D) (6 , 9)

E) (9 , 11)

The position of moving object does not change between t = 1 s and t = 4 s and therefore the velocity is equal to zero in this interval of time.

Answer B.

The graph of the position x versus time t of a moving object is shown in figure 1 above . At what time was the object furthest from the origin (x = 0)?

A) t = 1 s

B) t = 4 s

C) t = 6 s

D) t = 9 s

E) t = 11 s

At t = 9 s, x = -15 m and this is the furthest point from x = 0.

Answer D.

The graph of the position x versus time t of a moving object is shown in figure 1 above . Over which time interval(s) was the object moving in the negative direction?

A) (6 , 11)

B) (0 , 1)

C) (1 , 4)

D) (4 , 11)

E) (4 , 9)

From t = 4 s to t = 9 s, x is decreasing and therefore the velocity is negative which means the object is moving in the negative direction.

Answer E.

The graph of the position x versus time t of a moving object is shown in figure 1 above . Over which time interval(s) was the object moving in the positive direction?

A) (0 , 1) and (9 , 11)

B) (0 , 6)

C) (1 , 4) and (6 , 11)

D) (0 , 4) and (4 , 9)

E) (0 , 11)

In both intervals 0 to 1 and 9 to 11, x is increasing, the velocity is positive and therefore the object is moving in the positive direction.

Answer A.

Question 5 to 10 refer to the displacement vs time below.

The graph of the velocity v versus time t of a moving object is shown in figure 2 above. What is the total displacement from t = 0 to t = 9 seconds?

A) -2.5 m

B) 2.5 m

C) 0 m

D) 9 m

E) 15 m

The displacement is given by the area between the t-axis and the graph of the velocity.

Area of Trapezoid on the left below t-axis = -(1/2)(4 + 2)(2.5) = -7.5

Area of Triangle on the right above t-axis = (1/2)(3)(5) = 7.5

total displacement from t= 0 to t = 9 = Total area = -7.5 + 7.5 = 0

Answer C.

The graph of the velocity v versus time t of a moving object is shown in figure 2 above. What is the total distance covered by the object from t = 0 to t = 9 seconds?

A) 9 m

B) 5 m

C) 7.5 m

D) 30 m

E) 15 m

Between t = 0 and t = 4, the object is moving in the negative direction (velocity negative). The distance is given by the absolute value of the displacement which is given by the area.

distance from (t=0 to t=4) = | -(1/2)(4 + 2)(2.5) | = 7.5

Between t = 6 and t = 9, the object is moving in the positive direction (velocity positive). The distance is given by the absolute value of the displacement which is given by the area.

distance from (t = 6 to t = 9) = | (1/2)(3)(5) | = 7.5

total distance from (t= 0 to t = 9) = 7.5 + 7.5 = 15 m

Answer E.

The graph of the velocity v versus time t of a moving object is shown in figure 2 above. What is the average velocity over the interval t = 0 to t = 9 seconds?

A) 0.6 m/s

B) 0 m/s

C) 5 m/s

D) 1.5 m/s

E) 9 m/s

average velocity = displacement / time = 0 / 9 = 0

Answer B

The graph of the velocity v versus time t of a moving object is shown in figure 2 above. What is the average speed over the interval t = 0 to t = 9 seconds?

A) 1.7 m/s

B) 9 m/s

C) 5 m/s

D) 7.5 m/s

E) 15 m/s

average speed = distance / time = 15 / 9 = 1.7 m/s (rounded to 2 sf)

Answer A

The graph of the velocity v versus time t of a moving object is shown in figure 2 above. Over which time interval(s) was the object accelerating uniformly?

A) (6 , 9)

B) (4 , 6)

C) (3 , 4) and (6 , 7)

D) (0 , 1) and (7 , 9)

E) (0 , 9)

Answer C

The graph of the velocity v versus time t of a moving object is shown in figure 2 above. Over which time interval(s) was the acceleration of the object equal to zero?

A) (1 , 4)

B) (4 , 7)

C) (1 , 4)

D) (6 , 9)

E) (1 , 3) and (4 ,6)

Answer E

Question 11 to 12 refer to the acceleration vs time below.

The graph of the acceleration v versus time t of a moving object is shown in figure 3 above. Over which time interval(s) was the object accelerating uniformly?

A) (0 , 9)

B) (0 , 2)

C) (2 , 4)

D) (2 , 9)

E) (4 , 8)

Answer B

The graph of the acceleration v versus time t of a moving object is shown in figure 3 above. Over which time interval(s) was the object decelerating uniformly?

A) (0 , 2)

B) (2 , 4)

C) (8 , 9)

D) (4 , 8)

E) (2 , 9)

Answer D