A cheetah and an antelope are 100 m apart. The cheetah spots the antelope and runs towards it.

Question 13

A cheetah and an antelope are 100 m apart. The cheetah spots the antelope and runs towards it. The antelope reacts to the cheetah after one second and runs directly away from the cheetah. Both animals take 2 seconds to reach their top speeds. The graph shows how the speeds of the two animals vary with time.

How far apart are the animals, 17 seconds after the cheetah began running?

A 4 m              B 11 m                        C 54 m                        D 89 m

Reference: Past Exam Paper – November 2015 Paper 13 Q8

Solution:

Answer: B.

The antelope is 100 m ahead of the cheetah. The initial separation between the two animals is 100 m. They did not start at the same position.

Distance travelled is given by the area under the speed-time graph.

Area of trapezium = ½ × sum of parallel sides × height

Distance travelled by cheetah after 17s = ½ × (17+15) × 29

Distance travelled by cheetah after 17s = 464 m

Distance travelled by antelope after 17s = ½ × (16+14) × 25

Distance travelled by antelope after 17s = 375 m

However, the antelope was already 100 m ahead before running.

So, distance of antelope = 375 + 100 = 475 m

Separation of the animals after 17 s = 475 – 464 = 11 m