Worksheet: Uniform Linear Motion

Practice

In this worksheet, we will practice solving rate problems using the formula d = rt, where d represents distance, r represents rate, and t represents time.

Q1:

A cyclist travelled east at 15 m/s for 15 seconds, and then he stopped to rest for 10 seconds. Then, he moved west at 2 m/s for 75 seconds. Find the cyclist’s average speed for the whole trip.

Q2:

Two cars left travelling to a city, 𝐡 , 54 km away from city 𝐴 at the same time. If the speed of the first car was 40 km/h, and the second car was moving at 60 km/h, how long will the second car wait at city 𝐡 for the first car to arrive?

Q3:

Two cars were moving in opposite directions on a road between 𝐴 and 𝐡 . The first car started at point 𝐴 and travelled at 104 km/h, and the second started at point 𝐡 and travelled at 100 km/h. Given that the points 𝐴 and 𝐡 are 153 km apart, determine the time 𝑑 and the distance 𝑑 from point 𝐴 at which the two cars met.

  • A 𝑑 = 7 8 k m , 𝑑 = 8 0 m i n
  • B 𝑑 = 7 5 k m , 𝑑 = 4 5 m i n
  • C 𝑑 = 7 6 . 5 k m , 𝑑 = 9 0 m i n
  • D 𝑑 = 7 8 k m , 𝑑 = 4 5 m i n
  • E 𝑑 = 7 6 . 5 k m , 𝑑 = 2 2 . 5 m i n

Q4:

A train travelling with a uniform speed of 180 km/h passed through a tunnel in 18 seconds. Given that the train was 210 metres long, find the length of the tunnel.

Q5:

A motorcycle started moving from a point 𝐴 at a uniform speed. Given that, after 3 minutes, it was 2 km from 𝐴 , and, after 8 minutes, it was 18 km from the same point, determine the speed of the motorcycle.

Q6:

If a body covered 𝑑 meters in 10 minutes with a uniform velocity of 44 m/min, find the time taken to cover this distance when the body moves with a velocity of 20 m/min.

  • A 44 minutes
  • B 5 minutes
  • C 9 minutes
  • D 22 minutes

Q7:

Maged starts walking along a path at a constant 4 mph. One and a half hours after Maged leaves, his sister Rania starts jogging along the same route at a constant 6 mph. How long will it take Rania to catch up with Maged?

Q8:

A man was walking on a railway bridge 𝐴 𝐡 , which starts at point 𝐴 . He heard the whistle of a train coming from beyond point 𝐴 after he had covered 1 5 of the bridge’s length. The train was heading towards him at a uniform speed of 20 km/h. Given that, at a certain speed, the man could either run towards 𝐴 and narrowly avoid the train there or run towards 𝐡 and narrowly avoid the train there, what is the minimum uniform speed that he must move with in order to avoid being hit by the train?

  • A 28 km/h
  • B 220 km/h
  • C 16 km/h
  • D 12 km/h
  • E 4 km/h

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