a car traveled at uniform velocity of 20m/sec for 5 sec the brakes are applied and car s uniformly and come to rest in further 8 sec.find
a)distance traveled in first five sec
b)distance traveled after breaks are applied
c)total displacement during this period and its avrage velocity in whole journy.
(a) s1 =v•t =20•5 =100 m,
(b)
v(final) =v - a•t
v(final) =0
a =v/t,
s =v•t - at²/2 =
= v•t - v•t²/2•t =v•t/2=20•8/2=80 m
(c)
s =s1+s2 = 100+80 = 180 m
(d)
v(ave) = s/t =180/(8+5) = 13.85 m/s.
Kch nahi
To find the answers to these questions, we need to use the equations of motion for uniform velocity and uniform acceleration.
a) Distance traveled in the first five seconds:
Since the car is traveling at a uniform velocity of 20 m/s for 5 seconds, we can use the formula:
Distance = Velocity × Time
So, the distance traveled in the first five seconds is:
Distance = 20 m/s × 5 s = 100 meters
b) Distance traveled after the brakes are applied:
After the brakes are applied, the car decelerates uniformly and comes to rest. The time taken for this is 8 seconds, and we need to find the distance traveled during this time.
To calculate the distance, we can use the equation of motion:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
Since the car comes to rest, the final velocity is 0 m/s. Therefore, the equation becomes:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
Since the initial velocity is 20 m/s and the time is 8 seconds, we can substitute these values into the equation:
Distance = 20 m/s × 8 s + (1/2) × Acceleration × (8 s)^2
Since the car comes to rest, the final velocity is 0 m/s:
0 = 20 m/s + (1/2) × Acceleration × (8 s)
Simplifying this equation, we get:
160 m/s = 4 s × Acceleration
Therefore, the acceleration is:
Acceleration = 160 m/s ÷ 4 s = 40 m/s^2
Now, we can substitute the values of initial velocity, time, and acceleration into the equation to find the distance:
Distance = 20 m/s × 8 s + (1/2) × 40 m/s^2 × (8 s)^2
Simplifying this equation, we get:
Distance = 160 m + 320 m = 480 meters
So, the distance traveled after the brakes are applied is 480 meters.
c) Total displacement during this period and its average velocity in the whole journey:
To find the total displacement, we need to consider the distances traveled in the first five seconds and after the brakes are applied.
Total displacement = Distance traveled in the first five seconds + Distance traveled after the brakes are applied
Total displacement = 100 meters + 480 meters
Total displacement = 580 meters
The average velocity is given by the formula:
Average velocity = Total displacement / Total time
Since the total time is the sum of the time traveled at uniform velocity (5 seconds) and the time traveled after the brakes are applied (8 seconds), we can substitute the values:
Average velocity = 580 meters / (5 s + 8 s)
Average velocity = 580 meters / 13 seconds
Average velocity = 44.62 m/s (rounded to two decimal places)
So, the total displacement during this period is 580 meters, and the average velocity for the whole journey is 44.62 m/s.