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Chapter 6: Q.38 (page 156)

A 5.0 Kg object initially at rest at the origin is subjected to the time-varying force shown below. What is the object鈥檚 velocity at $t = 6 s e c .$ ?

Short Answer

Expert verified

The objects velocity is 4 m/s.

Step by step solution

01

Given information

Mass of object at rest $(m) = 5.0 k g$

time $(t) = 6 s$

02

Explanation

We know that the expression for velocity is given by

$V = a t (I) w h e r e, V = v e l o c i t y a = a c c e l e r a t i o n t = t i m e$

and According to Newton's second law,

$F = m a S o, a = \frac{F}{m} (I I)$

where,

f= force, m= mass, a= acceleration

Substituting $(I I)$ in $(I)$ we get the formula needed to find the velocity

i.e.

$V = \frac{F}{m} 脳 t (I I I)$

The value $F 脳 t$ can be calculated from the given graph triangular area.

(i.e.,) The area of triangle $= F 脳 t = \frac{1}{2} 脳 4 脳 10 = 20 N s$

Now by Substituting the values in the equation ( $I I I$ ), we get

$V = \frac{20}{5 k g} V = 4 m / s$

The object's velocity is $4 m / s$

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