Question

The Position of a particle moving along x axis is given by x=t^3+t^2+t+1 m find. (1) position of particle at t= 0 sec ,at 2 sec,at 3 sec,at 10 sec . ​​

Answer 1

Given :

➳ Relation b/w position and time has been provided.

$\bigstar\:\underline{\boxed{\tt{t^3+t^2+t+1}}}$

To Find :

➨ Position of particle at

• t = 0s
• t = 2s
• t = 3s
• t = 10s

Solution :

⇒ We can simply solve this question by putting value of t in given position-time equation.

✪ Position at t = 0 s :

$\longrightarrow\tt\:x=t^3+t^2+t+1\\ \\ \longrightarrow\tt\:x_0=(0)^3+(0)^2+(0)+1\\ \\ \longrightarrow\underline{\boxed{\bf{x_0=1m}}}$

✪ Position at t = 2 s :

$\longrightarrow\tt\:x=t^3+t^2+t+1\\ \\ \longrightarrow\tt\:x_2=(2)^3+(2)^2+(2)+1\\ \\ \longrightarrow\tt\:x_2=8+4+2+1\\ \\ \longrightarrow\underline{\boxed{\bf{x_2=15m}}}$

✪ Position at t = 3 s :

$\longrightarrow\tt\:x=t^3+t^2+t+1\\ \\ \longrightarrow\tt\:x_3=(3)^3+(3)^2+(3)+1\\ \\ \longrightarrow\tt\:x_3=27+9+3+1\\ \\ \longrightarrow\underline{\boxed{\bf{x_3=40m}} }$

✪ Position at t = 10 s :

$\longrightarrow\tt\:x=t^3+t^2+t+1\\ \\ \longrightarrow\tt\:x_{10}=(10)^3+(10)^2+(10)+1\\ \\ \longrightarrow\tt\:x_{10}=1000+100+10+1\\ \\ \longrightarrow\underline{\boxed{\bf{x_{10}=1111m}}}$