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VashaNatasha [74]
3 years ago
10

An object has a position given by the radius vector r = [2.0 m + (3.00 m/s)t](i)+ [3.0 m - (2.00 m/s^2)t^2](j). Here (i) and (j)

are the unit vectors along x and y and all quantities are in SI units. What is the speed and magnitude of the acceleration in m/s^2 of the object at time t = 2.00 s
Physics
1 answer:
jenyasd209 [6]3 years ago
3 0

Answer:

The speed of the object is (3i - 4.00tj)m/s

The magnitude of the acceleration is 4.00m/s²

Explanation:

Given - position vector;

r = (2.0 + 3.00t)i + (3.0 - 2.00t²)j       -------------------(i)

To get the speed vector (v), take the first derivative of equation (i) with respect to time t as follows;

v = \frac{dr}{dt}

 v = \frac{d[(2.0 + 3.00t)i + (3.0 - 2.00t^2)j]  }{dt}  

v  = 3i - 4.00tj      ------------------------(ii)

To get the acceleration vector (a), take the first derivative of the speed vector in equation(ii) as follows;

a = \frac{dv}{dt}

a = \frac{d(3i - 4.00tj)}{dt}

a = -4.00j

The magnitude of the acceleration |a| is therefore given by

|a| = |-4.00|

|a| = 4.00 m/s²

In conclusion;

the speed of the object is (3i - 4.00tj)m/s

the magnitude of the acceleration is 4.00m/s²

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