Question

Worked out solution

2/115 The car C increases its speed at the constant rate of 1.5 m/s2 as it rounds the curve shown. If the mag- nitude of the total acceleration of the car is 2.5 m/s2 at the point A where the radius of curva- ture is 200 m, compute the speed v of the car at this point Problem 2/115

Answer 1

total acceleration(a) = sqrt(at^2 + an^2)

here,given

at = tangetial acceleration = 1.5 m/sec^2

an = normal acceleration = ??

a = 2.5 m/sec^2

So,

an = sqrt(a^2 - at^2)

an = sqrt(2.5^2 - 1.5^2)

an = 2 m/sec^2

Since,

an = (v^2)/r

given radius of curvature(r) = 200 m

So,

velocity of car at point A (v) = sqrt(an*r)

v = sqrt(2*200)

v = 20 m/sec.

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