Stopping distance of
vehicles : When brakes are applied to a
moving vehicle, the distance it travels before
stopping is called stopping distance. It is
an important factor for road safety and
depends on the initial velocity (v0
) and the
braking capacity, or deceleration, –a that
is caused by the braking. Derive an
expression for stopping distance of a vehicle
in terms of vo
anda.
Galileo’s law of odd
numbers : “The distances traversed, during
equal intervals of time, by a body falling
from rest, stand to one another in the same
ratio as the odd numbers beginning with
unity [namely, 1: 3: 5: 7……].” Prove it.
Galileo’s law of odd
numbers : “The distances traversed, during
equal intervals of time, by a body falling
from rest, stand to one another in the same
ratio as the odd numbers beginning with
unity [namely, 1: 3: 5: 7……].” Prove it.
Free-fall : Discuss the
motion of an object under free fall. Neglect
air resistance.
A ball is thrown vertically
upwards with a velocity of 20 m s–1 from
the top of a multistorey building. The
height of the point from where the ball is
thrown is 25.0 m from the ground. (a) How
high will the ball rise ? and (b) how long
will it be before the ball hits the ground?
Take g = 10 m s–2
.
Obtain equations of motion
for constant acceleration using method of
calculus.
The position of an object
moving along x-axis is given by x = a + bt2
where a = 8.5 m, b = 2.5 m s–2 and t is
measured in seconds. What is its velocity at
t = 0 s and t = 2.0 s. What is the average
velocity between t = 2.0 s and t = 4.0 s ?
Figure 2.15 gives a speed-time graph of
a particle in motion along a constant
direction. Three equal intervals of time
are shown. In which interval is the
average acceleration greatest in
magnitude? In which interval is the
average speed greatest ? Choosing the
positive direction as the constant
direction of motion, give the signs of v
and a in the three intervals. What are
the acceleration at the points A, B, C
and D ?
Figure 2.14 gives the x-t plot of a
particle in one-dimensional motion.
Three different equal intervals of time
are shown. In which interval is the
average speed greatest, and in which
is it the least ? Give the sign of average
velocity for each interval.
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