A car starts from rest on a curved road of radius 200 m and attains a speed of 18 km/hr at the end of 60 seconds while travelling with constant tangential acceleration. What will be the normal acceleration of car after 30 seconds from the start?

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BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

When a body moves along a curved path with constant tangential acceleration, the total acceleration has two components:

1. Tangential acceleration due to change in speed.

2. Normal (centripetal) acceleration due to change in direction, given by:

\( a_n = \frac{v^2}{r} \)

Calculation:

Given:

Final speed after 60 seconds: v = 18 km/h = 5 m/s

Radius of curve: r = 200 m

Time = 60 s, Initial speed = 0 (starts from rest)

Step 1: Calculate tangential acceleration

\( a_t = \frac{v - u}{t} = \frac{5 - 0}{60} = \frac{1}{12}~m/s^2 \)

Step 2: Speed at 30 seconds:

\( v = a_t \times t = \frac{1}{12} \times 30 = 2.5~m/s \)

Step 3: Normal acceleration

\( a_n = \frac{v^2}{r} = \frac{(2.5)^2}{200} = \frac{6.25}{200} = 0.03125~m/s^2 \)