A motor car moving at a
speed of 72 km/hr can not
see to a stop in less than 3
seconds while for a truck this
time interval is 5 seconds
On a highway, the car is
behind the truck, both
moving al 72 km/hr The
truck gives a signal that it is
going to stop at emergency
At whal distance the car
should be from the truck so
that it does not bump onto
(collide with) the truck
Human response time is 0. 5 second
Answers
Answer:
Given that;
Speed of both car and truck,
v=
72 km/h
or,
v=
20 m/s
Time taken to stop the car after applying the break,
t
c
=
3.0 s
Time taken to stop the truck after applying the break
=
t
t
=
5.0 s
Therefore,
Retardation of the car, a
c
=
3
0−20
= −
3
20
m/s
2
Retardation of the truck, a
t
=
5
0−20
= −4 m/s
2
Let at time
t=
0
, the truck signals to stop and applies the break.
At time
t=
0
, let the truck and the car be at a distance
s m from each other.
Time taken by the car to travel
s m=
t
seconds.
To avoide the bump, the velocity of the car and the truck after time t should be equal.
Thus,
Velocity of the truck after time t :
v
t
= u− at
v
t
= 20− 4t
The car will apply the break after 0.5 seconds of signal.
Thus;
Velocity of car after time t will be:
v
c
= u− a(t− 0.5)
v
c
= 20−
3
20
(t− 0.5)
Therefore,
20− 4t= 20−
3
20
(t− 0.5)
t=
4
5
sec
Thus,
Distance travelled by truck in time t
s
t
= ut+
2
1
at
2
s
t
= 20×
4
5
−
2
1
× 4×
(
4
5
) 2
s
t
=21.875
Distance travelled by the car in t seconds, s
s
;
Distance travelled by the car in 0.5 s + distance travelled by the car in
(t−
0.5)sec
s
s
= 20× 0.5+ 20×
(
4
5
−
2
1
) −
2
1
×
3
20
×
(
5
4
−
2
1
) 2
s
s
= 23.125
Therefore, minimum distance required for the car to be distant from the truck will be
23.125−
21.875=
1.25 m
hope it's help you
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✒️Your Question :-
➡️ A motor car moving at a
speed of 72 km/hr can not
see to a stop in less than 3
seconds while for a truck this
time interval is 5 seconds
On a highway, the car is
behind the truck, both
moving al 72 km/hr The
truck gives a signal that it is
going to stop at emergency
At whal distance the car
should be from the truck so
that it does not bump onto
(collide with) the truck
Human response time is 0. 5 second