Acceleration

A car and a bus are side by side at the traffic lights. They are both stationary. The lights turn to green.Thirty seconds later the bus and the car are at the same speed of 15m/s (approx 30 mph)

The car however is ahead of the bus.

a)     Does the car have a higher speed than the bus?

b)    How much does the car’s speed go up?

c)     How much does the bus’ speed go up

d)    Which took less time to reach 15 m/s the car or the bus?

e)     Which has the higher acceleration the car or the bus?

f)     Does acceleration just depend upon changing speed? (More than yes or no is required here)

Calculations

1.       Jerry is standing in the middle of the room Tom runs around the corner. Jerry accelerates to 5m/s in 3 s. Calculate the value of his acceleration.

a = (v-u)/t = (5-0)/3 = 1.67 ms^-2

2.       Tom is just behind Jerry when he runs into a mouse hole. Tom hits the wall at a speed of 6m/s. He comes to rest in 0.2s. Calculate the acceleration of Tom’s head. Does the collision kill Tom?

a = (v-u)/t = (0-6)/0.2 = -30 ms^-2   No, cartoon characters follow the laws of “Wile E Coyote Physics”

3.       At the end of a 215km race Mark accelerates from 18m/s to 21 m/s in 1.2s. Calculate his acceleration.

a = (v-u)/t = (21-18)/1.2 = 2.5 ms^-2

4.       Jeremy pushes the pedal to the metal once again. His reasonably priced car takes 13.6 seconds to accelerate from 13m/s to 47m/s. Calculate his acceleration.

a = (v-u)/t = (47-13)/13.6 = 2.5 ms^-2

5.       Thomas is puffing along at 25m/s when the signal ahead turns to red. He applies his brakes and slows to 11m/s in 35s. Calculate his acceleration.

a = (v-u)/t = (11-25)/35 = -0.4 ms^-2

6.       An oil tanker’s top speed is 6.7 m/s. If it decelerates at 0.005m/s². Calculate how long it takes to stop.

a = (v-u)/t

rearranging t = (v-u)/a

t = (0 – 6.7)/ - 0.005

t = 1340s = 22 min

Distance = t(v-u)/2 = 1340(0-6.7)/2 = 4489m = 4.5km

7.       At take off the Lunar Module had an acceleration of 3.4 m/s². The moon’s gravitational field will accelerate objects at 1.8m/s². Calculate the velocity of the Eagle 3s after lift off from Tranquillity Base.

a = (v-u)/t, 

rearranging (v-u) = at, 

(v-0) = (3.4 – 1.8) 3

v = 4.8 ms^-1

8.       At 11.40pm on the 14^th April 1912 the Titanic was running at 22 knots (11.3 m/s) when it hit an iceberg. It is popular lore that the iceberg was spotted 37 seconds before the ship hit it. After the disaster tests were performed on its sister ship the Olympic. At 18 knots (9.2 m/s) it took 3 min 15 seconds to stop. Calculate the deceleration of The Olympic.

a = (v-u)/t  a= (0-9.2)/(3 x 60) +15, a = -9.2/195 = -0.05 ms^-2

Assume the Titanic decelerated at the same rate, and the officers on the bridge had reacted immediately. Calculate it’s velocity after 37 seconds of deceleration.

a = (v-u)/t,

rearranging  (v-u)= at,

(v – 11.3) = -0.05 x 37,

(v – 11.3) = -1.74,

v = 11.3 – 1.74 = 9.6 ms^-2

(The 37 seconds was calculated after the event. It was the time needed for the Titanic to have swerved away from the iceberg)