Question

A car travels at a rate of 30 km/h for 5 minutes and then at 40 km/h for 10 minutes. Find (i) the total distance travelled by the car and (ii) the average speed of the car.

Answer 1

Concept:

Speed Distance time relation and the average speed which is total distance covered divide by total time.

Given:

Speed of car for 5 minutes is 30 Km/hr

Speed of car for 10 minutes is 40 Km/hr

Find:

Total Distance Travelled

Average Speed of car

Solution:

5 Minutes = 5 × 60 seconds

5 Minutes = 300 seconds

30 Km/hr = 30×(5/18) m/s

30 Km/hr = 8.33 m/s

Similarly

10 Minutes = 10 × 60 seconds

10 Minutes = 600 seconds

40 Km/hr = 40×(5/18) m/s

40 Km/hr = 11.11 m/s

Speed of car in first 5 minutes = 30 Km/hr

Speed of car in first 300 = 8.33 m/s

Speed = Distance / time

Distance in (300 sec) = Speed × time

Distance in (300 sec) = 8.33 × 300

Distance in (300 sec) = 2499 metres

Speed of car in next 10 minutes = 40 Km/hr

Speed of car in next 600 = 11.11 m/s

Speed = Distance / time

Distance in (600 sec) = Speed × time

Distance in (600 sec) = 11.11 × 600

Distance in (600 sec) = 6666 metres

Total Distance covered will be = 2499 + 6666 metres

Total Distance covered will be = 9165 metres

which is also

Total Distance covered will be = 9.165 Kilo metres

Average speed = Total Distance / Total Time

Total Distance = 9165 Km

Total Time = 300 + 600 seconds

Total time = 900 seconds

Average speed = 9165 / 900 m/s

Average speed = 10.18 m/s

Average speed = 36.64 Km/hr

So we can conclude that by applying the concepts of Kinematics we calculated that the Total distance covered is 9.165 Km and average speed is 36.64 Km/hr

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Answer 2

Answer:

By using the principles of kinematics, we were able to determine that the total distance travelled was 9.165 km, and the average speed was

36.66 km/h.

Explanation:

The ratio of the entire distance travelled by the individual to the amount of time it took to complete that distance can be used to calculate average speed.

Car travels at 30 km/hr for five minutes.

The average car's 10 minute speed is 40 km/h.

Distance Traveled Overall

average vehicle speed

speed during $AB = 30 km/h$

                             $=\frac{30*1000}{60*60}$

                              $=\frac{25}{3} m/s$

speed during $BC = 40 km/h$

                              $=\frac{40*1000}{60*60}$

                              $=\frac{100}{9} m/s$

Total distance $= AC = AB+BC$

                        $=\frac{25}{3} *5*60+\frac{100}{9} *10*60$

                        $= 2500 + 6666.667$

                        $= 9166.667 m$

average speed $=\frac{S_{1}*T_{1}+S_{2}*T_{2} }{T_{1}+T_{2} }$

                          $=\frac{150+400}{15}$

                          $= 36.66 km/h$

By using the principles of kinematics, we were able to determine that the total distance travelled was 9.165 km, and the average speed was

36.66 km/h.

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