Page 129 - Understanding NCERT Science 09

Let us now express the kinetic energy of Solution:
an object in the form of an equation. Consider
Mass of the object, m = 15 kg, velocity
an object of mass, m moving with a uniform –1
velocity, u. Let it now be displaced through a of the object, v = 4 m s .
From Eq. (10.5),
distance s when a constant force, F acts on it
in the direction of its displacement. From 1 2
Eq. (10.1), the work done, W is F s. The work E = 2 m v
k
done on the object will cause a change in its
velocity. Let its velocity change from u to v. = 1 × 15 kg × 4 m s × 4 m s –1
–1
Let a be the acceleration produced. 2
We studied three equations of motion. The = 120 J
relation connecting the initial velocity (u) The kinetic energy of the object is 120 J.
and final velocity (v) of an object moving
with a uniform acceleration a, and the
displacement, s is Example 10.4 What is the work to be done
2
v – u = 2a s to increase the velocity of a car from
2
–1
30 km h to 60 km h if the mass of
–1
This gives
the car is 1500 kg?
2
v – u 2
s = (10.2)
2a Solution:
From section 9.4, we know F = m a. Thus, Mass of the car, m =1500 kg,
using (Eq. 10.2) in Eq. (10.1), we can write the initial velocity of car, u = 30 km h –1
work done by the force, F as
30 × 1000m
2
v - u 2 =
W = m a ´ 60 × 60s
2a
–1
= 25/3 m s .
or
Similarly, the final velocity of the car,
1 2 2
W = m ( v – u ) (10.3) v = 60 km h –1
2
= 50/3 m s .
–1
If the object is starting from its stationary
position, that is, u = 0, then Therefore, the initial kinetic energy of
the car,
1 2
W = m v (10.4) 1
2 E = m u 2
ki
It is clear that the work done is equal to the 2
change in the kinetic energy of an object. 1
= × 1500 kg × (25/3 m s )
–1 2
1 2 2
If u = 0, the work done will be m v .
2 = 156250/3 J.
Thus, the kinetic energy possessed by an The final kinetic energy of the car,
object of mass, m and moving with a uniform
velocity, v is 1

–1 2
E = × 1500 kg × (50/3 m s )
1 2 kf 2
E = m v (10.5)
k
2 = 625000/3 J.
Thus, the work done = Change in
Example 10.3 An object of mass 15 kg is kinetic energy
moving with a uniform velocity of 4 = E – E
m s . What is the kinetic energy kf ki
–1
possessed by the object? = 156250 J.
118 SCIENCE

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