a particle has initial velocity of 9 m/s^2 and retardation of 2m/s^2.find the distance travelled in 5 th second

### Asked by trenuka180 | 14th May, 2021, 11:18: AM

Expert Answer:

### Velocity at end of 4^{th} second , v_{4} = v_{o} - ( a t ) = 9 - ( 2 × 4 ) = 1 m/s
Displacement at 5^{th} second , S = ( u t ) - [ (1/2) a t^{2} ] = ( 1 ×1 ) - ( 0.5 × 2 × 1 × 1 ) = 0
Above expression shows the displacement is zero .
Hence just after 5^{th }second particle moves forward with velocity 1 m/s then it is stopped then it turns back
in opposite direction if retardation continues.
Time taken for the particle to reach the zero speed after 5^{th} second is given as,
t = u/a = initial speed / acceleration = 1 / 2 = 0.5 s
Distance moved in 0.5 s after 5^{th} second , S = ( ut ) -(1/2) at^{2} = ( 1 × 0.5 ) - ( 0.5 × 2 × 0.5 × 0.5 ) = 0.25 m
Hence particle has moved 0.25 m forward and then 0.25 m backward
Total distance travelled = ( 0.25 + 0.25 ) m = 0.5 m

^{th}second , v

_{4}= v

_{o}- ( a t ) = 9 - ( 2 × 4 ) = 1 m/s

^{th}second , S = ( u t ) - [ (1/2) a t

^{2}] = ( 1 ×1 ) - ( 0.5 × 2 × 1 × 1 ) = 0

^{th }second particle moves forward with velocity 1 m/s then it is stopped then it turns back

^{th}second is given as,

^{th}second , S = ( ut ) -(1/2) at

^{2}= ( 1 × 0.5 ) - ( 0.5 × 2 × 0.5 × 0.5 ) = 0.25 m

### Answered by Thiyagarajan K | 14th May, 2021, 12:41: PM

## Concept Videos

- Derive an expression for average velocity and instantaneous velocity for the motion of an object in x-y plane.
- Particles moves a certain distance In a staright line as follows first 1/4th at V° next 1/2th at 2v2 last 1/4 th at v0 find avg speed
- from A to B speed is v⁰. From B to C during first half speed is v1 and during last half speed is v2 . Find Average Speed From A to C
- A passenger in a train with speed 72 km/h observed another train coming from the opposite direction with speed 32.4 km/h. What's the length of the second train if it crosses the passenger in 10s?
- the speed necessary to go into orbit around the earth is 8km/h.it is also necessary to travel about 200 km in order to get out of the atmosphere suppose a rocket can reach their speed after travelling 200 km under constant acceleration what could be the acceleration
- The numerical ratio of displacement to distance is
- a body travels from A to B at 40m/s and from B to A at 60m/s. calculate the average speed and average velocity of the object.
- A man takes 40 seconds to complete one circle .radius of the circle is 10metre. Find the displacement after 20 seconds?
- What is a frame of referen5

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change