Answer 2_1_7

Information:

• The maximum speed of the train is 25 m/s
• The time interval OX is 45 s
• The time interval XY is 45 s
• The time interval YC is 20 s         

What is:

a)      The acceleration between O and A:

Gradient of the graph gives the acceleration.  Gradient = rise/run 

Acceleration = 25 m/s = 0.56 m/s²

                            45 s

b)      The acceleration between B and C:

Again we use the gradient.  This time it's negative:

Acceleration = - 25 m/s = -1.25 m/s²

                                20 s

c)      The distance covered while the train is at constant speed:

This time we us the area under the graph.  We need to find the area of the rectangle ABXY:

Distance covered = 25 m/s × 45 s = 1125 m

d)      The total distance. 

This time we have to look at the total area under the graph.  We already know the area of the rectangle.  So we have to work out the area of the two triangles, OAX and BCY.

Area of OAX = 1/2 x 45 s x 25 m/s = 562.5 m

Area of BCY = 1/2 x 20 s x 25 m/s = 250 m

Total distance = 562.5 m + 1125 m + 250 m = 1937.5 m = 1940 m (3 s.f.)

e)   The average speed?   

Average speed = total distance = 1940 m = 17.7 m/s

                                   total time            110 s

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