A bus of mass 2000kg starts from rest and come down a hill with a constant acceleration . It travels a distance of 600m in 10 s . Find acceleration and force on it.
a) a =10m/s2 ,f 5000N
b) a = 12 m /s2 , f =24000N
c) a =12 m /s2 ,f = 10000N
d) None of these
Answers
Answer :
- Option (b)
- acceleration is 12 m/s²
- Force is 24000 N
Given :
- A bus of mass 2000 kg starts from rest and come down a hill a constant acceleration
- It travels a distance 600m in 10 s
To find :
- Acceleration
- Force
Solution :
Given ,
- Initial velocity (u) = 0 m/s
- Distance travelled (s) = 600m
- Time taken (t) = 10s
- Mass (m) = 2000 kg
- Acceleration (a) = ?
Now , we need to find the acceleration :
We know that 2nd equation of motion (acceleration) :
- s = ut + ½ at²
Where,
- S is distance travelled
- u is Initial velocity
- t is time taken
- a is acceleration
Substituting the value :
⇢ s = ut + ½ at²
⇢ 600 = 0 × 10 + ½ × a × (10)²
⇢ 600 = 0 + ½ × a × 100
⇢ 50a = 600
⇢ a = 600/50
⇢ a = 12m/s²
Acceleration (a) = 12 m/s².
Now , we need to find the force :
We know that,
- F = m × a
Where ,
- F is force
- m is mass
- a is acceleration
Given
- Mass is 2000 kg
- Acceleration is 12 m/s²
Now,
⇢ Force = Mass × acceleration
⇢ Force = 2000 × 12
⇢ Force = 24000 N
Hence, Force is 24000 N
Option is (b).
Given : A bus of mass 2000kg starts from rest and come down a hill with a constant acceleration .
It travels a distance of 600m in 10 s .
To Find : acceleration and force on it.
a) a =10m/s2 ,f 5000N
b) a = 12 m /s2 , f =24000N
c) a =12 m /s2 ,f = 10000N
d) None of these
Solution:
u = 0 ( rest)
a = ?
t = 10 s
S = 600 m
S = ut + (1/2)at²
=> 600 = 0 + (1/2)a (10)²
=> 600 = 50a
=> a = 12
Hence acceleration is 12 m/s²
F = ma
m = 2000 kg
a = 12 m/s²
F = 2000 * 12
=> F = 24000 N
Force is 24000 N
Correct option is b) a = 12 m /s² , F=24000N
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