10. The driver of a moving car suddenly sees ahead a very old man on the middle of the road. To save the old man he applies the brake, which produces an acceleration of 4 m/s² in opposite direction to the motion. After 3 seconds car comes to rest. (a) Calculate the initial velocity and distance travelled by the car. (b) If the man is 20 m away from the car, would the driver succeed to save the old man? Explain by calculation. (c) What value does the car driver show?
Answers
ANSWER:
a.)
1.) initial velocity of car = 12m/s
2.) distance travelled by car after applying brakes = 18 meter
________________
Explanation:
given that,
the driver brakes his moving car to save a women in front of the car
which produces an acceleration of 4 m/s² in opposite direction to the motion.
since,
force of brakes in the opposite direction of motion so,
it will deceleration = 4 m/s²
acceleration = -4 m/s²
also,
given that,
After 3 seconds car comes to rest.
so,
here,
time taken by brakes to stop the car = 3 seconds
final velocity of the car = 0 m/s [ since car stops ]
now,
a) 1.) Calculate the initial velocity.
let the initial velocity of car be u
we have,
initial velocity = u
final velocity(v) = 0 m/s
time (t) = 3 s
acceleration(a) = -4 m/s²
by the equation of motion
v = u + at
putting the values,
0 = u + (-4)(3)
u - 12 = 0
u = 12 m/s
so,
initial velocity of car = 12m/s
2.) distance travelled by the car after applying brakes.
let the distance travelled be s
now,
we have,
initial velocity(u) = 12 m/s
final velocity(v) = 0 m/s
acceleration(a) = -4 m/s²
now,
by the equation of motion
v² = u² + 2as
putting the values
(0)² = (12)² + 2(-4)s
-8s + 144 = 0
-8s = -144
s = -144/-8
s = 18 m
so,
distance travelled by car after applying brakes
= 18 meter
b.) If the man is 20 m away from the car, would the driver succeed to save the old man?
➡yes he must save the old man because old man is 20 m far from car and
after applying brakes the car stops 2 meter further than the old man
so, he will be saved
c.) What values does the car driver shows?
The car driver shows the kindness by saving the life of the old man
____________________
Given data :-
Acceleration in negative direction :- 4 m/s^2
▪ Acceleration in negative direction means deceleration
▪ a = - 4
Time taken = 3 seconds
===================
(a) Calculate the initial velocity and distance travelled by the car.
Solution :-
Initial velocity (u) = ?
Final velocity (v) = 0
v = u + at
0 = u + (-4) × 3
U - 12 = 0
U = 12m/s^2
》 Distance
S = ut + 1/2 at^2
S = 12 (3) + 1/2 (-4)(3)^2
S = 36 + 1/2 (-4)(9)
S = 36 + 1/2 (-36)
S = 36 - 36/2
S = 36 - 18
S = 18m
So the Distance travelled is 18 m and initial velocity is 12 m/s^2
=====================
. (b) If the man is 20 m away from the car, would the driver succeed to save the old man? Explain by calculation.
Solution :- The driver will definitely save the old man because the driver stops at 18 m and the old man is 2m far from it i.e at 20 m
====================
(c) What value does the car driver show?
Car drive shows HUMANITY . it's a small word but means a lot . He shows his kindness towards the old man
'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'-'
Extra info :-
For solving any problems like this we must know 3 equations of uniform acceleration
They are :-