Question

2. A car starts from rest and accelerates at 2 m/s2 for
5 seconds, then travels at a steady speed for
another 5 seconds, in same direction. The distance
it has covered for entire 10 seconds is
(1) 50 m
(2) 25 m
(3) 40 m
(4) 75 m​

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

Case-1

u = 0 m/s.

a = 2 m/s².

t = 5 seconds.

Distance = ${S_1}$

Case-2

a = 0 m/s²

(As it moves in steady speed

so, differentiating a constant velocity gives zero acceleration)

t = 5 seconds.

Distance = ${S_2}$

$\huge{\bold{\underline{Explanation:-}}}$

Case-1

Applying second kinematic equation.

$\large{\bold{S = ut + \frac{1}{2}at^2}}$

Substituting the values.

$\large{S_1 = 0 + \frac{1}{2} \times 2 \times (5)^2}$

$\large{S_1 = \frac{1}{ \cancel{2}} \times \cancel{2} \times 25}$

$\large{S_1 = 25 \: m}$

Final velocity before it starts motion with uniform speed.

Applying First kinematics equation.

$\large{\bold{v = u + at}}$

Substituting the values.

$\large{v = 0 + 2 \times 5}$

$\large{v = 10 \: m/s}$

Case-2

As the body starts motion with uniform speed the final Speed in case-1 will be initial Speed in case-2 .

Applying second kinematic equation.

$\large{\bold{S = ut + \frac{1}{2} at^2}}$

Substituting the values.

$\large{S_2 = 10 \times 5 + 0}$

as acceleration is zero.

$\large{S_2 = 50 \:m}$

Total distance covered by the body.

$\large{\bold{S = S_1 + S_2}}$

$\large{S = 25 + 50}$

$\huge{\boxed{\boxed{S = 75 \: m}}}$

So,the distance travelled by the body in entire 10 seconds is 75 meters

(Option - 4).