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(4) Te8. A car is travelling with linear velocity v on a circular road of radius r. If the speed is increasing at tof 'a' metre/sec2, then the resultant acceleration will be -v2+ a2VL |
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Answer» IThe instantaneous acceleration pointing towards the center of the circle is called centripetal acceleration. It is denoted by 'a₍r₎'It's magnitude is given asa₍r₎ = v²/rwhere 'r' is the radius of curvature.The tangential component cause a change in its speed and it's magnitude is given asa₍t₎ = dv/dt = a m/s²Hence, tangential acceleration is,a₍t₎ = a m/s²Now,Resultant acceleration = a² = a₍r₎² + a₍t₎²Putting the values , we get:Resultant acceleration = a² = (v²/r)² + a²Resultant acceleration = a² = v⁴/r² + a²Resultant acceleration = a = √ (v⁴/r² + a²)which is the required answer. |
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