Physics: The velocity of a projectile is given by v={16t2i+4t3j+(5t+2)k} m/s, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle’s acceleration (ms/2) when t = 2 s.

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The velocity of a projectile is given by v={16t2i+4t3j+(5t+2)k}

Ответ:

austinbeesley9855

19.01.2022

Physics

The acceleration will be 117 m/s².

Explanation:

The function of velocity is given as

v = 16t² i + 4t³j+5tk+2k

As acceleration is the measure of rate of change in velocity with respect to time, the differentiation of the function of velocity with respect to time will give us the function for acceleration.

Since ,the basic formula for derivation is $\frac{d(x^{n} )}{dt} = nx^{n-1}$

This above equation is applicable only when x is a function of t and x is a non-singular function. Also, the power n should be greater than 0.

So,

$\frac{dv}{dt}=(2*16)t+(3*4)t^{2} +5$

So, $Acceleration = \frac{dv}{dt}= 32t+12t^{2} +5$

Since, the time t is given as 2 s, then if we substitute this value in the above equation, we get

Acceleration = (32*2)+(12*2*2)+5

So acceleration = 64+48+5 = 117 m/s².

Thus, the acceleration will be 117 m/s².

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The velocity of a projectile is given by v={16t2i+4t3j+(5t+2)k} m/s, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle’s acceleration (ms/2) when t = 2 s.

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