Page 33 - Physics Coursebook 2015 (A level)

Chapter 2: Accelerated motion
WORKED EXAMPLES
4 The rocket shown in Figure 2.12 lifts off from rest with an acceleration of 20 m s−2. Calculate its velocity after 50 s.
Step 3 Calculation then gives: v2 = 64 + 36 = 100 m2 s−2
v = 10ms−1
So the car will be travelling at 10 m s−1 when it stops
accelerating.
(You may find it easier to carry out these calculations withoutincludingtheunitsofquantitieswhenyou substitute in the equation. However, including the units can help to ensure that you end up with the correct units for the final answer.)
6 A train (Figure 2.14) travelling at 20 m s−1 accelerates at 0.50ms−2for30s.Calculatethedistancetravelledbythe train in this time.
u = 20 m s–1
Figure 2.14 For Worked example 6. This train accelerates for 30 s.
Step 1 What we know: andwhatwewanttoknow:
u = 0ms−1 a = 20ms−2
t = 50s v = ?
Step2 Theequationlinkingu,a,tandvisequation1: v = u + at
Substituting gives: v = 0+(20×50)
Step3 Calculationthengives: v = 1000 m s−1
So the rocket will be travelling at 1000 m s−1 after 50 s. This makes sense, since its velocity increases by 20 m s−1 every second, for 50 s.
You could use the same equation to work out how long the rocket would take to reach a velocity of 2000 m s−1, or the acceleration it must have to reach a speed of 1000ms−1 in 40s, and so on.
5 The car shown in Figure 2.13 is travelling along a straight road at 8.0 m s−1. It accelerates at 1.0 m s−2 for a distance of 18 m. How fast is it then travelling?
u = 20ms−1 t = 30s
Step3 Calculationthengives: s = 600+225=825m
So the train will travel 825 m while it is accelerating.
Step 1 What we know:
andwhatwewanttoknow:
Step2 Theequationweneedisequation3: s = u t + 12 a t 2
Substituting gives:
s = (20 × 30) + 12 × 0.5 × (30)2
u = 8.0 m s–1
v = ?
a = 0.50ms−2 s = ?
Figure2.13 ForWorkedexample5.Thiscaraccelerates for a short distance as it travels along the road.
In this case, we will have to use a different equation, because we know the distance during which the car accelerates, not the time.
Step 1 What we know: andwhatwewanttoknow:
u = 8.0ms−1 a = 1.0ms−2
s = 18 m
v = ? Step2 Theequationweneedisequation4:
v2 = u2 + 2as
Substituting gives:
v2 = 8.02 +(2×1.0×18)
s = 18 m
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