Question

1. A bus starting from rest moves
with a uniform acceleration of
0.1 m s2 for 2 minutes. Find (a)
the speed acquired, (b) the
distance travelled.
109​

Answer 1

a. 12 m/s

b. 720 m

GIVEN:

• Acceleration, a = 0.1 m/s²
• Time , t = 2 minutes
• Since the bus is initially at rest, initial velocity, u = 0

TO FIND:

• a. Speed acquired, v (final velocity)
• b. Distance travelled, s

FORMULAE:

• According to first equation of motion, v = u + at

• According to second equation of motion, s = ut + (at²)/2

SOLUTION:

STEP 1: To convert time in standard unit

• SI unit of time is seconds.
• 1 minute = 60 seconds.
• 2 minutes = 2 × 60 seconds
• Time, t = 120 seconds

STEP 2: To find speed.

$v = u + at \\ \\ v = 0 + (0.1 \times 120) \\ \\ v = 0.1 \times 120 \\ \\ v = 12 \: \frac{m}{s}$

The speed acquired is 12 m/s.

STEP 3: To find distance

$s = ut + \frac{1}{2} a {t}^{2} \\ \\ s = (0 \times 120) + ( \frac{1}{2} \times 0.1 \times {(120)}^{2} ) \\ \\ s = 0 + ( \frac{1}{2} \times 0.1 \times 120 \times 120 ) \\ \\ s = \frac{12 \times 120}{2} \\ \\ s = 6 \times 120 \\ \\ s = 720 \: m$

Distance travelled is 720 m.

ANSWERS:

• a. The speed acquired is 12 m/s.
• b. Distance travelled is 720 m.

OTHER FORMULA:

According to third equation of motion, v²- u² = 2as

Distance travelled can also be found using this formula, when yhe speed acquired v is known.

v²- u² = 2as

(12)² - 0² = 2 × 0.1 × s

144 = 0.2 × s

s = 144 / 0.2

s = 1440 / 2

s = 720 m