Question

if the velocity of a car moving with uniform velocity changes from 25 m/s to 50 m/s in 10 second . a) what is the acceleration of the car .b) what is the displacement by the car during the time interval.​

Answer 1

$\sf \pmb{Answer :}$

Given :

Final velocity, v = 50 m/s

Initial velocity, u = 25 m/s

Time, t = 10 seconds

To find :

Acceleration, a &

Displacement, s

According to the question,

➞ v = u + at

Where,

v = Final velocity

u = Initial velocity

a = Acceleration

t = Time

➞ Substituting the values,

➞ 50 = 25 + a × 10

➞ 50 - 25 = 10a

➞ 25 = 10a

➞ 25 ÷ 10 = a

➞ 2.5 = a

So,the acceleration is 2.5 m/s².

➞ s = ut + ½ at²

Where,

a = Acceleration

u = Initial velocity

v = Final velocity

s = Distance/ Displacement

➞ s = 25 × 10 + ½ × 2.5 × 10 × 10

➞ s = 250 + 2.5 × 5 × 10

➞ s = 250 + 125

➞ s = 375

So,the displacement of the car during the time interval is 375 meters.

Answer 2

Given:

Velocity of a car moving with uniform velocity changes from 25 m/s to 50 m/s in 10 second.

To Find:

What is the acceleration of the car & displacement by the car during the time interval.

Solution:

Here we have:

$</p><p>\sf{Final \: Velocity \: (v) = 50 \: m/s}FinalVelocity(v)=50m/s$

$\sf{Initial \: Velocity \: (v) = 25 \: m/s}InitialVelocity(v)=25m/s$

$\sf{Time \: (t) = 10 \: sec}Time(t)=10sec$

★According to question. now:

We know the first equation of motion:

$\boxed{\tt\green\star \: {v = u + at}}$

Substituting values in our Equation:

$\begin{gathered} \\ :\implies\rm{50 = 25 + a \times 10} \\ \\ </p><p>:\implies\rm{50 - 25 = 10a} \\ \\ :\implies\rm{25 = 10a} \\ \\ :\implies\rm{a = \dfrac{\cancel{25}}{\cancel{10}}} \\ \\ :\implies{\boxed{\sf{\red{a = 2.5}}}} \: \bigstar\end{gathered}:⟹50=25+a×10:⟹50−25=10a:⟹25=10a:⟹a=1025:⟹a=2.5★</p><p>$

We know the second equation of motion:

Substituting values in our Equation:

$\begin{gathered}\\ :\implies\rm{s = 25 \times 10 + \frac{1}{2} \times 2.5 \times 10 \times 10} \\ \\ :\implies\rm{s = 250 + 2.5 \times 5 \times 10} \\ \\ :\implies\rm{s = 250 + 125} \\ \\ :\implies{\boxed{\sf{\blue{s = 375}}}} \: \bigstar\end{gathered}:⟹s=25×10+21×2.5×10×10:⟹s=250+2.5×5×10:⟹s=250+125:⟹s=375★$

Thus,

therefore∴ The acceleration of the car is 2.5 m/s² and the displacement of the car is 375 meters.