Question

A bus of mass 500 kg is moving with a velocity of 5 m/s and is acted upon by a forward force of 500 N due to engine and retarding force of 200 N due to friction. Find the velocity of the bus after 20 sec.

Answer 1

Given :

⟶ Mass of bus = 500kg

⟶ Initial velocity of bus = 5m/s

⟶ Force due to engine = 500N

⟶ Retarding force = 200N

⟶ Time = 20s

To Find :

➾ Final velocity of bus after the given interval of time.

Concept :

➳ This question is completely based on the concept of Newton's second law of motion.

➳ As per this law, Net force acts on the moving object is defined as the rate of change of linear momentum.

Mathematically,

$\bigstar\:\underline{\boxed{\bf{F=\dfrac{\Delta P}{\Delta t}}}}$

➳ Momentum is defined as the product of mass and velocity.

Calculation :

$\longrightarrow\tt\:F_{net}=\dfrac{m(v-u)}{t}\\ \\ \longrightarrow\tt\:(500-200)=\dfrac{500(v-5)}{20}\\ \\ \longrightarrow\tt\:300=25(v-5)\\ \\ \longrightarrow\tt\:v-5=\dfrac{300}{25}=12\\ \\ \longrightarrow\tt\:v=12+5\\ \\ \longrightarrow\underline{\boxed{\bf{v=17\:ms^{-1}}}}\:\gray{\bigstar}$

Answer 2

★Question:–

A bus of mass 500 kg is moving with a velocity of 5 m/s and is acted upon by a forward force of 500 N due to engine and retarding force of 200 N due to friction. Find the velocity of the bus after 20 sec.

★Answer:–

Given mass of the bus (m)=500 kg

Velocity of bus(u)=5m/s

Forward force (F)=500 N

Frictional force (F)=200N

Time(t)=20s

Net force ,F'=500-200 =300N.

Let v be the velocity after 20s

From relation,

$F = \frac{m(v - u)}{t}$

$300 = \frac{500(v - 5)}{20}$

$6000 = 500v - 2500$

$500v - 2500 = 6000$

$500v = 6000 + 2500$

$500v = 8500$

$v = \frac{8500}{500}$

$v = 17m/s$

The velocity of bus after 20 sec is 17 m/s.