A particle traveling in a circular path of radius 300 m has an instantaneous velocity of 30 m/s and its velocity is increasing at a constant rate of 4 m/s2. What is the magnitude of its total acceleration at this instant?

a. 3 m/s2
b. 4 m/s2
c. 5 m/s2
d. -5 m/s2

(c) 5m/s²

Total acceleration (a) of a particle in a circular motion is the vector sum of the radial or centripetal acceleration () of the particle and the tangential acceleration () of the particle and its magnitude can be calculated as follows;

a =           ---------------------(i)

But;

=      ------------------------------(ii)

Where;

v = instantaneous velocity

r =  radius of the circular path of motion

From the question;

v = 30m/s

r = 300m

(i) First let's calculate the centripetal acceleration by substituting the values above into equation (ii) as follows;

=

=

= 3m/s²

(ii) From the question, the velocity of the particle is increasing at a constant rate of 4m/s²  and that is the tangential acceleration , of the particle. i.e;

= 4m/s²

(iii) Now substitute the values of and into equation (i) as follows;

a =

a =

a =

a = 5m/s²

Therefore, the magnitude of its total acceleration a, is 5m/s²

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