Question

The velocity-time graph of a particle in one dimensional motion is shown in figure below.
which of the following formulae are correct for describing the motion of the particle over the time-interval $t_1 to t_2$:
a. $x(t_2)=x(t_1)+ V_{t_1}(t_2-t_1)+\frac{1}{2}a(t_2-t_1)^{2}$
b. $v(t_2)=v(t_1)+ a(t_2-t_1)$
c. $V_{average}=\frac{(x(t_2)-x(t_1))}{t_2-t_1}$
d. $V_{average}=\frac{(x(t_2)-x(t_1))}{t_2-t_1}$
e. $x(t_2)=x(t_1)+ V_{average}(t_2-t_1)+\frac{1}{2}(t_2-t_1)^{2}$
f. $x(t_2)=x(t_1)$ = area under the v-t curve bounded by the axis and the dotted line shown.

Answer 1

Hii dear,

# Answer- (c), (d) & (f)

# Explaination-
- Acceleration of the particle is given by slope of the graph.
- Here, we can observe that the graph has non-uniform slope indicating acceleration varying with time.
- Hence only formulas for non-uniform motion will apply here.
- Options (a), (b) & (e) are for uniform motion and so can't be applied here.
- Only formulas (c), (d) & (f) correctly describe the motion.

Hope that is useful...