Practice on Speed, Velovity, and Acceleration: Solution-1

Question 1: A quantity used to measure how the velocity changes over time is called
Answer: acceleration.

Question 2: A school child throws a ball downward from rest and then realized that the ball covers a distance of 1.0 m in a time of 5.0 s.
Calcualte the ball's acceleration.
Answer: 0.8 m/s2
Explanation:
Average velocity = 1 m / 5 s = 0.20 m/s, average velocity during 5 s.
The initial velocity was zero and the final velocity is more than 0.20 m/s.
Since average velocity = (initial velocity + final velocity)/ 2 = 0.20 m/s,
this implies that final velocity = 2 × average velocity − 2 × initial velocity = 0.40 m/s.
Acceleration = change in velocity / total time = (0.4 m/s - 0) / 5 s = 0.8 m/s2


Question 3: A motorbike runs 50 meters in the first two seconds from point A to point B, then runs 60 more meters from B to C in the next two seconds, and finally, runs for 70 meters from C to D in the last two seconds. Calculate the acceleration of the motorbike.
Answer: 2.5 m/s2
Explanation:
Let's note distance by d, time by t, speed by v and acceleration by a
d = vi × t + ½ × a × t2
So, from A to B, equation (1): 50 m = vi × 2 + ½ × a × 22
From A to C, d = 50 m + 60 m = 110 m and t = 2 s + 2 s = 4 s; hence equation (2); 110 m = vi × 4 + ½ × a × 42
From equation 1), vi = 25 − a; replacing this in equation 2); vi4 + ½a16 = 110 is equivalent to 100 − 4a + 8a = 110
We obtain a = 2.5 m/s2 and vi = 25 - 2.5 = 22.5 m/s.
Let's double check these findings in equation 3 which is from A to D where d = 50 + 60 + 70 = 180 m and t = 2 s + 2 s + 2 s = 6 s
d = vi × 6 + ½ × a × 62 = 22.5 m/s × 6 s + ½ × 2.5 m/s2 × 36 s = 135 m + 45 m = 180 m
This is exactly what distance is between A and D.

Question 4: A motorbike starts from rest, and then goes through a contant acceleration and travels a distance of 1000 meters.
The motorbike reaches a final speed of 100 meters/second.
Calcualte the time it takes the motorbike to cover 1000 meters.
Answer: 10 s

Explanation:
time = speed / distance = 1000 / 100 = 10 s

Question 5: Assume a boat traveling at constant speed
Answer: can change direction.

Question 6: A school child throws a ball downward from rest and then realized that the ball covers a distance of 2.0 m in a time of 4.0 s.
Calculate the ball's average speed.
Answer: 0.5 m/s.
Explanation:
average speed = total distance / total time = 2 m / 4 s = 0.5 m/ s

Question 7: Which two quantities will always have the same magnitude?
Answer: instantaneous speed and instantaneous velocity.

Question 8: Which of the following quantities relating to motion is not a vector?
Answer: speed.

Question 9: A car starts from rest and reaches 40 m/s in 10 seconds.
The average acceleration of the car is
Answer: 4 m/s2

Explanation:
average speed = change in velocity divided by elapsed time = (40 m/s − 0 m/s) / (10 s − 0 s) = 4 m/s2



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Date of last modification: 2021