Question

15. A car travels along a straight line for first half time with speed 40km/hr and the second

half time with speed 60km/hr. Find the average speed of the car.

16. A body starts rolling over a horizontal surface with an initial velocity of 0.5m/s. Due to

friction, its velocity decreases at the rate of 0.05m/s2. How much time will it take for the

body to stop?

17. A car traveling at 36km/hr speeds up to 70km/hr in 5 seconds. What is its acceleration? If

the same car stops in 20s, what is the retardation?

18. A scooter acquires a velocity of 36km/hr in 10seconds just after the start. It takes 20

seconds to stop. Calculate the acceleration in the two cases

Answer 1

HI !

15. A car travels along a straight line for first half time with speed 40km/hr and the second half time with speed 60km/hr. Find the average speed of the car.
Ans :-
S1 = 40 km/hr
S2 = 60 km/hr

S = S1+ S2
= 100 km/hr

Time = 2 hrs

Average speed = 100/2
= 50 km/hr
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16)A body starts rolling over a horizontal surface with an initial velocity of 0.5 m/s. Due to friction, its velocity decreases at the rate of 0.05 m/s². How much time will it take for the body to stop?

Initial velocity = u = 0.5 m/s
Final velocity = v = 0

Acceleration = a = -0.05 m/s² [ retardation]

Time = t
v = u + at
0 = 0.5 + -0.05 × t
-0.5 = -0.05t

t = 0.5/0.05
= 10 sec

Time taken to stop = 10 sec
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17) A car traveling at 36 km/hr speeds up to 70 km/hr in 5 seconds. What is its acceleration? If the same car stops in 20 s, what is the retardation?

Initial velocity = u = 36km/hr = 36 x 5/18 = 10 m/s
Final velocity = v = 70 km/hr = 70 x 5/18 = 19.4 m/s
Time = t = 5 sec

acceleration = a = v - u /t
= 19.4-10/5
= 1.88 m/s²

=============================
t = 20 sec

Initial velocity = u = 19.4 m/s
Final velocity = v = 0 m/s

acceleration = 0-19.4/20
= -0.97 m/s²

Hence ,
the retardation = -0.47 m/s²
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18. A scooter acquires a velocity of 36 km/hr in 10 seconds just after the start. It takes 20 seconds to stop. Calculate the acceleration in the two cases

Case 1 :-
Initial velocity = u = 0
Final velocity = v = 36 km/hr = 10 m/s
Time = t = 10 s

Acceleration = a = (v - u) / t
= (10 - 0) / 10
= 10/10
= 1 m/s²

Acceleration in case 1 is 1 m/s²
----------------------

Case 2:-
Initial velocity = u = 36 km/h = 10 m/s
Final velocity = v = 0 m/s
Time = t = 20 s

Acceleration = a = (v - u) / t
= (0 - 10) / 20
= -10/20
= - 0.5 m/s²

Acceleration in this case is - 0.5 m/s².
Negative sign indicates retardation

Answer 2

Heya,

15. Let , Time taken to travel 40km/hr be t/2 as it has taken half time

Speed = distance / time

40 km/hr = distance / t/2

Distance travelled = 40 × t/2

= 20t

The time taken to travel 60 km/hr = t/2 as it is the other half time

Speed = Distance/ time

60km/hr = distance / t/2

Distance = 60× t/2

= 30t

Average speed =(20t+ 30t)/t

= 50t/t

= 50 km /hr

16. Given,

Initial velocity u) =0.5 m/s

Final velocity (v) = 0 

Retardation = 0.05 m/s ²

V = u + at

0 = 0.5 + 0.05 t

Time taken = 0.5/0.05
= 10 sec

Time taken by the body to stop = 10 sec

17. Case 1:-

Initial velocity (u) = 36 km/hr

Final velocity (v) = 70 km /hr 

⇒ u = 10 m/s and v= 19.4 m/s

a = (v-u)/t

= 9.4 / 5

=1.88 m/s²

Case 2 :-

u = 19.4 m/s

v = 0

V = u+ at

0 = 19.4 + 20 a

-19.4 = 20 a

a = -19.4/20

= -0.97 m/s ²

Retardation of the car = 0.97 m/s ²

18. Case 1:-

u = 0 m/s

v = 36 km/hr = 10 m/s

Time taken = 10 sec

a = v-u /t

= 1 m/s²

∴Acceleration of the scooter = 1 m/s²

Case 2:-

u = 36 km/hr = 10m/s

v = 0

Time taken = 20 seconds

a= -10m/s/20 sec

= -0.5 m/s²

∴ Retardation = -0.5 m/s²

Hope it helps u.........