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A car is travelling with a linear velocity v m/sec on a circular road . If its speed is increasing at the rate of a m/sec, then how to calculate the resultant acceleration

A car is travelling with a linear velocity v m/sec on a circular road . If its speed is increasing at the rate of a m/sec, then how to calculate the resultant acceleration

Grade:11

1 Answers

Manas Shukla
102 Points
7 years ago
As the question suggests , car’s linear acceleration is a m/s2 . To elaborate consider time interval 1 sec and apply the formula v = u + at , we get
v+a = v + accelration x 1 , Thus linear accelration = a.
Now we know the centripetal force for car = m x v^2 / r , where v is the velocity of car and r = radius of circular path.
Thus centripetal acceleration = v^2 / r , 
Total acceleration = root of (linear acc^2 + centripetal acc^2) , 
thus Total acc = root of (a^2 + (v^4 / r^2))

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